Cancellation of Join in Boolean Algebra

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

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


 * $a \vee c = b \vee c$
 * $a \vee \neg c = b \vee \neg c$

Then $a = b$.

Proof
Hence the result.

Also see

 * Cancellation of Meet in Boolean Algebra