Cancellation of Meet in Boolean Algebra

Theorem
Let $\left({S, \vee, \wedge, \neg}\right)$ be a Boolean algebra.

Let $a, b, c \in S$, and suppose that:

Then $a = b$.

Proof
Follows from Cancellation of Join in Boolean Algebra through the Duality Principle

Also see

 * Cancellation of Join in Boolean Algebra