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In CodePen, whatever you write in the HTML editor is what goes within the <body> tags in a basic HTML5 template. So you don't have access to higher-up elements like the <html> tag. If you want to add classes there that can affect the whole document, this is the place to do it.

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CSS

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HTML 

              
                <script id="templCard" type="x-tmpl-mustache">
  <li class="stacked-cards__card card form-card">
    <div class="form-card__img"></div>
    <div class="form-card__content">
      Vraag 1 van 4:<br/>
      <b>Wat is je geboortedatum?</b>
    </div>
  </li>
</script>
<script id="templQ2" type="x-tmpl-mustache">
  <li class="stacked-cards__card card form-card">
    <div class="form-card__img"></div>
    <div class="form-card__content">
      <div class="form-card__progress">Vraag 2 van 5:</div>
      <div class="form-card__question">Wat is je beroep?</div>
      <div class="form-card__input">
        <input type="text" class="form__input" placeholder="Kies een beroep"></input>
      </div>
      <div class="form-card__info">Staat je beroep er niet bij? Neem dan contact met ons op. We helpen je graag verder.</div>
    </div>
  </li>
</script>
<script id="templQ3" type="x-tmpl-mustache">
  <li class="stacked-cards__card card form-card">
    <div class="form-card__img"></div>
    <div class="form-card__content">
      <div class="form-card__progress">Vraag 3 van 5:</div>
      <div class="form-card__question">Welk bedrag wil je verzekeren?</div>
      <div class="form-card__input">
        <input type="text" class="form__input" placeholder="Bruto jaarbedrag"></input>
      </div>
      <div class="form-card__info">Dit is het bruto bedrag per jaar en is bij deze verzekering maximaal €45.000. Wil je een hoger bedrag verzekeren? Neem dan contact met ons op.</div>
    </div>
  </li>
</script>
<script id="templQ4" type="x-tmpl-mustache">
  <li class="stacked-cards__card card form-card">
    <div class="form-card__img"></div>
    <div class="form-card__content">
      <div class="form-card__progress">Vraag 4 van 5:</div>
      <div class="form-card__question">Hoe lang kun je zonder uitkering?</div>
      <div class="form-card__input">
        <input type="radio" name="days" id="14days" value="14"></input>
        <label class="form__radio" for="14days">14 dagen</label>
        <input type="radio" name="days" id="30days"></input>
        <label class="form__radio" for="30days" value="30">30 dagen</label>
        <input type="radio" name="days" id="60days"></input>
        <label class="form__radio" for="60days" value="60">60 dagen</label>
      </div>
    </div>
  </li>
</script>
<script id="templQ5" type="x-tmpl-mustache">
  <li class="stacked-cards__card card form-card">
    <div class="form-card__img"></div>
    <div class="form-card__content">
      <div class="form-card__progress">Vraag 5 van 5:</div>
      <div class="form-card__question">Wat is je gewenste uitkeringsduur?</div>
      <div class="form-card__input">
        <input type="radio" name="years" id="2years" value="2"></input>
        <label class="form__radio" for="2years">2 jaar</label>
        <input type="radio" name="years" id="5years"></input>
        <label class="form__radio" for="5years" value="5">5 jaar</label>
      </div>
    </div>
  </li>
</script>
<script id="templSummary" type="x-tmpl-mustache">
  <li class="stacked-cards__card card summary">
    <div class="summary__text">Uit deze gegevens blijkt dat je het beste af bent met een AOV 2.5. Wijzig hieronder je gegevens of sluit hem direct af.</div>
    <ul class="summary__list">
      <li class="summary__item">
        Geboortedatum: 18-06-1985
        <button type="button" class="summary__edit-btn"></button>
      </li>
      <li class="summary__item">
        Beroep: Consulant
        <button type="button" class="summary__edit-btn"></button>
      </li>
      <li class="summary__item">
        Verzekerd bedrag: € 2000
        <button type="button" class="summary__edit-btn"></button>
      </li>
      <li class="summary__item">
        Looptijd: 2 jaar
        <button type="button" class="summary__edit-btn"></button>
      </li>
      <li class="summary__item">
        Overbruggingsperiode: 30 dagen
        <button type="button" class="summary__edit-btn"></button>
      </li>
    </ul>
  </li>
</script>
<div class="container">  
  <div class="stacked-cards">
    <ul class="stacked-cards__stack js-stacked-cards">
      <li class="stacked-cards__card card premium">
        <div class="premium__content">
          <div class="premium__title">AOV premie voor jouw situatie</div>
          <div class="premium__amount">€ 35,56</div>
          <div class="premium__footer">Bruto p.m.</div>
          <a href="#" class="premium__details">Bekijk details en premieverloop</a>
        </div>
      </li>
      <li class="stacked-cards__card card form-card">
        <div class="form-card__img"></div>
        <div class="form-card__content">
          <div class="form-card__progress">Vraag 1 van 5:</div>
          <div class="form-card__question">Wat is je geboortedatum?</div>
          <div class="form-card__input">
            <input type="text" class="form__input" placeholder="DD-MM-JJJJ"></input>
          </div>
        </div>
      </li>
      <li class="stacked-cards__card card" data-card-id="templQ2">
        <div class="card__loader"></div>
      </li>
      <li class="stacked-cards__card card" data-card-id="templQ3">
        <div class="card__loader"></div>
      </li>
      <li class="stacked-cards__card card" data-card-id="templQ4">
        <div class="card__loader"></div>
      </li>
      <li class="stacked-cards__card card" data-card-id="templQ5">
        <div class="card__loader"></div>
      </li>
      <li class="stacked-cards__card card" data-card-id="templSummary">
        <div class="card__loader"></div>
      </li>
    </ul>
    <div class="stacked-cards__nav">
      <div class="stacked-cards__prev">
        <button type="button" class="stacked-cards__prev-btn js-prev">
          <svg xmlns="http://www.w3.org/2000/svg" width="24" height="16" viewBox="0 0 24 16">
              <path fill="#FFF" fill-rule="evenodd" d="M20.374 8.518l-.152-.009H.805a.805.805 0 0 1 0-1.61h19.417l.132-.008-.133-.16-5.639-5.278a.824.824 0 0 1-.02-1.185.869.869 0 0 1 1.217-.012l7.022 6.75a.952.952 0 0 1 .122.142.91.91 0 0 1-.003 1.115.952.952 0 0 1-.118.137l-7.022 6.751a.869.869 0 0 1-1.237-.034.822.822 0 0 1 .042-1.162c3.361-3.124 5.24-4.883 5.636-5.279.048-.048.099-.101.153-.158z"/>
          </svg>
        </button>
      </div>
      <div class="stacked-cards__next">
        <button type="button" class="stacked-cards__next-btn js-next">
          <svg xmlns="http://www.w3.org/2000/svg" width="24" height="16" viewBox="0 0 24 16">
              <path fill="#FFF" fill-rule="evenodd" d="M20.374 8.518l-.152-.009H.805a.805.805 0 0 1 0-1.61h19.417l.132-.008-.133-.16-5.639-5.278a.824.824 0 0 1-.02-1.185.869.869 0 0 1 1.217-.012l7.022 6.75a.952.952 0 0 1 .122.142.91.91 0 0 1-.003 1.115.952.952 0 0 1-.118.137l-7.022 6.751a.869.869 0 0 1-1.237-.034.822.822 0 0 1 .042-1.162c3.361-3.124 5.24-4.883 5.636-5.279.048-.048.099-.101.153-.158z"/>
          </svg>
        </button>
      </div>
    </div>
  </div>
</div>
!

CSS 

              
                $diff: 4px;
$border-radius: 8px;
$duration: 0.4s;

* {
  box-sizing: border-box;
}

body {
  background-color: #9cd4ef;
  font-family: Arial;
  margin: 4rem 0;
}

.container {
  width: 100%;
  max-width: 500px;
  margin-left: auto;
  margin-right: auto;
  padding-left: 1rem;
  padding-right: 1rem;
}

input[type=radio] {
  display: none;
}

.premium {
  display: flex;
  flex-direction: column;
  
  &__content {
    overflow-x: hidden;
    position: relative;
    flex-grow: 1;
    border-top-left-radius: 8px;
    border-top-right-radius: 8px;
    text-align: center;
    color: white;
    
    &:before {
      content: '';
      border-radius: 50%;
      height: 420px;
      width: 130%;
      position: absolute;
      left: 50%;
      top: 0;
      background-color: #ff8d00;
      transform: translate(-50%, -45%);
      z-index: -1;
    }
  }
  
  &__title {
    font-size: 16px;
    line-height: 19px;
    margin-top: 2.25rem;
    margin-bottom: 1rem;
  }
  
  &__amount {
    font-size: 46px;
    margin-bottom: 0.5rem;
  }
  
  &__footer {
    
  }
  
  &__details {
    color: #1b94d8;
    position: absolute;
    bottom: 0.75rem;
    right: 0.75rem;
  }
}

.form {
  &__input {
    border: solid 1px #dedddd;
    border-radius: 2px;
    font-size: 14px;
    line-height: 22px;
    padding: 0.75rem 1rem;
    margin-top: 1rem;
    width: 100%;
    outline: 0;
    
    &:hover, &:focus {
      border-color: gray;
    }
  }
  
  &__radio {
    cursor: pointer;
    display: block;
    border-bottom: 1px solid #d8d8d8;
    margin-left: -1rem;
    margin-right: -1rem;
    padding: 1.25rem;
    padding-left: 3.75rem;
    position: relative;
    
    &:before {
      border: solid 1px #dedddd;
      border-radius: 50%;
      content: '';
      position: absolute;
      height: 30px;
      width: 30px;
      left: 1rem;
      top: 50%;
      transform: translateY(-50%);
    }
    
    &:hover:before {
      border-color: gray;
    }
    
    input[type=radio]:checked + &:after {
      border-radius: 50%;
      content: '';
      background-color: #ff8d00;
      height: 20px;
      width: 20px;
      left: calc(1rem + 6px);
      top: 50%;
      transform: translateY(-50%);
      position: absolute;
    }
    
    &:last-child {
      border-bottom: 0;
    }
  }
}

.card {
  &__loader {
    position: absolute;
    left: 50%;
    top: 50%;
    transform: translate(-50%, -50%);
    height: 50px;
    width: 50px;
    background-image: url(https://i.vimeocdn.com/portrait/16638942_300x300);
    background-size: contain;
    animation: loader 1.5s infinite;
    transform-origin: 50% 50%;
  }
}

.form-card {
  display: flex;
  flex-direction: column;
  
  &__img {
    background-image: url(https://www.amersfoortse.nl/-/media/images/ondernemer/hero-ondernemer-de-amersfoortse.png);
    background-size: cover;
    background-position: center center;
    border-top-left-radius: $border-radius;
    border-top-right-radius: $border-radius;
    height: 114px;
  }
  
  &__content {
    padding: 1rem;
    padding-bottom: 0.5rem;
    display: flex;
    flex-direction: column;
    flex-grow: 1;
    line-height: 19px;
  }
  
  &__progress, &__question {
    font-size: 14px;
  }
  
  &__question {
    font-weight: bold;
  }
  
  &__input {
    flex-grow: 1;
  }
  
  &__info {
    font-size: 12px;
    margin-bottom: 1rem;
  }
}

.summary {
  font-size: 14px;
  line-height: 19px;
  
  &__text {
    padding: 1rem 1rem 1.75rem;
  }
  
  &__list {
    list-style-type: none;
    padding: 0;
  }
  
  &__item {
    border-top: 1px solid #d8d8d8;
    padding: 1rem;
    padding-right: 2rem;
    position: relative;
  }
  
  &__edit-btn {
    content: '';
    cursor: pointer;
    position: absolute;
    border: 0;
    padding: 0;
    background-color: transparent;
    background-image: url(https://image.flaticon.com/icons/svg/61/61456.svg);
    background-size: contain;
    height: 16px;
    width: 16px;
    right: 1rem;
    top: 50%;
    transform: translateY(-50%);
  }
}

.stacked-cards {
  margin-bottom: 1rem;
  
  &__stack {
    list-style-type: none;
    padding-left: 0;
    position: relative;
    margin: 0 0 1rem;
  }
  
  &__card {
    background-color: white;
    border-radius: $border-radius;
    position: absolute;
    left: 0;
    right: 0;
    margin: 0 auto;
    min-height: 367px;
    transition: all $duration ease-in-out;
    
    &:nth-child(1) {
      box-shadow: 0 22px 44px -10px rgba(0, 0, 0, 0.28);
      top: 0;
      margin-left: 0;
      margin-right: 0;
      z-index: 4;
      position: relative;
    }
    
    &:nth-child(2) {
      bottom: -($diff * 1);
      margin-left: $diff * 1;
      margin-right: $diff * 1;
      z-index: 3;
    }
    
    &:nth-child(3) {
      bottom: -($diff * 2);
      margin-left: $diff * 2;
      margin-right: $diff * 2;
      background-color: #e1e1e1;
      box-shadow: 0 9px 14px -10px rgba(0, 0, 0, 0.14);
      z-index: 2;
    }
    
    &:nth-child(1n+4) {
      bottom: -($diff * 3);
      margin-left: $diff * 3;
      margin-right: $diff * 3;
      background-color: #e1e1e1;
      box-shadow: 0 9px 14px -10px rgba(0, 0, 0, 0.14);
      opacity: 0;
      z-index: 1;
    }
  }
  
  &__nav {
    display: flex;
  }
  
  &__prev {
    flex-grow: 1;
  }
  
  &__prev-btn, &__next-btn {
    border: 0;
    background-color: rgba(27,148,216, 1);
    border-radius: 50%;
    height: 48px;
    width: 48px;
    cursor: pointer;
    position: relative;
    outline: 0;
    transition: background-color 0.3s;
    
    &[disabled] {
      background-color: rgba(27,148,216, 0.2);
      cursor: default;
    }
    
    svg {
      position: absolute;
      left: 50%;
      top: 50%;
      transform: translate(-50%, -50%);
    }
  }
  
  &__prev-btn {
    transform: rotateY(180deg);
  }
  
  &--next {
    .stacked-cards__card {      
      &:nth-child(1) {
        animation: swipeCard $duration;
        
        @media screen and (max-width: 768px) {
          animation: swipeCardPortable $duration;
        }
      }
      
      &:nth-child(2) {
        box-shadow: 0 22px 44px -10px rgba(0, 0, 0, 0.28);
        bottom: 0;
        margin-left: 0;
        margin-right: 0;
      }

      &:nth-child(3) {
        bottom: -($diff * 1);
        margin-left: $diff * 1;
        margin-right: $diff * 1;
      }

      &:nth-child(4) {
        bottom: -($diff * 2);
        margin-left: $diff * 2;
        margin-right: $diff * 2;
        background-color: #e1e1e1;
        box-shadow: 0 9px 14px -10px rgba(0, 0, 0, 0.14);
      }      
    }
  }
  
  &--prev {
    .stacked-cards__card {      
      &:nth-child(1) {
        animation: swipeCard $duration;
        animation-direction: reverse;
        z-index: 6;
        
        @media screen and (max-width: 768px) {
          animation: swipeCardPortable $duration;
          animation-direction: reverse;
        }
      }    
    }
  }
}

@keyframes swipeCardPortable {
  0% { transform: translateX(0) rotate(0); } 
  100% { transform: translateX(-500px) rotate(-45deg); } 
}

@keyframes swipeCard {
  0% { transform: translateX(0) rotate(0); opacity: 1; } 
  30% { opacity: 1; }
  80% { opacity: 0; }
  100% { transform: translateX(-500px) rotate(-45deg); opacity: 0; } 
}

@keyframes loader {
  0% { transform: translate(-50%, -50%) rotate(0deg); }
  80% { transform: translate(-50%, -50%) rotate(360deg); }
}
!

JS 

              
                var cardTpl = $('#templCard').html();

function enablePrevBtn() {
  $('.js-prev').attr('disabled', false);
}

function disablePrevBtn() {
  $('.js-prev').attr('disabled', true);
}

function enableNextBtn() {
  $('.js-next').attr('disabled', false);
}

function disableNextBtn() {
  $('.js-next').attr('disabled', true);
}

function disableBtns() {
  disablePrevBtn();
  disableNextBtn();
}

function enableBtns() {
  enablePrevBtn();
  enableNextBtn();
}

function prevCard() {
  var $this = $(this),
      $nextBtn = $('js-next'),
      $stacked = $('.js-stacked-cards');
  
  disableBtns();
  
  $stacked.one('animationend', onAnimationEnd);
  $stacked.prepend(cardTpl);
  $stacked.addClass('stacked-cards--prev');
  
  function onAnimationEnd() {
    $stacked.removeClass('stacked-cards--prev');
    $this.attr('disabled', false);
    
    enableBtns();
  }
}

function nextCard() {
  var $this = $(this),
      $prevBtn = $('js-prev'),
      $stacked = $('.js-stacked-cards');
  
  disableBtns();
  
  setTimeout(nextResponseHandler, 1500);
  
  $this.attr('disabled', true);
  $prevBtn.attr('disabled', true);
  
  $stacked.children().eq(1).addClass('js-active');
  $stacked.one('animationend', onAnimationEnd);
  $stacked.addClass('stacked-cards--next');
  
  function onAnimationEnd() {
    $stacked.children().first().remove();
    $stacked.removeClass('stacked-cards--next');
    
    enablePrevBtn();
    
    if($stacked.children().length > 1) {
      enableNextBtn();
    }
  }
}

function nextResponseHandler() {
  var $active = $('.js-active'),
      id = $active.data('card-id'),
      tpl = $('#' + id).html();
  
  $active.replaceWith(tpl);
}

function bind() {
  $(document)
    .on(
      'click',
      '.js-prev',
      prevCard
    )
    .on(
      'click',
      '.js-next',
      nextCard
    );
}

bind();
!
999px

Console