Cancellation of Meet in Boolean Algebra

Theorem

Let $\struct {S, \vee, \wedge, \neg}$ be a Boolean algebra.

Let $a, b, c \in S$.

Let:

$\ds a \wedge c$

$=$

$\ds b \wedge c$

$\ds a \wedge \neg c$

$=$

$\ds b \wedge \neg c$

Then:

$a = b$

$\blacksquare$