A Common Principle of Boolean Algebra as Stated in George Boole's 'Mathematical Analysis of Logic':
A Common Principle of Boolean Algebra: xy = y

Statement of the Common Principle:
Should:
x = U
or, in other words:
x = 1
Then, in Boolean Notation :
xy = y
Or, in formal-logic notation:
x ∧ y = y
.
e.g. 1:
Let:
x = 1
.
Let:
y = 0
.
Hence:
xy = y
Or, in formal-logic notation:
x ∧ y = y
, because:
1 × 0 = 0
, or:
1(0) = 0
, or, in formal-logic notation:
1 ∧ 0 = 0
.
e.g. 2:
Let:
x = 1
.
Let:
y = 1
.
Hence:
xy = y
Or, in formal-logic notation:
x ∧ y = y
, because:
1 × 1 = 1
, or:
1(1) = 1
, or, in formal-logic notation:
1 ∧ 1 = 1
.
Addendum:
You may read George Boole's Mathematical Analysis of Logic, for free at Project Gutenberg