Operations of Boolean Algebra are Idempotent

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

Then:


 * $\forall x \in S: x \wedge x = x = x \vee x$

That is, both $\vee$ and $\wedge$ are idempotent operations.

Proof
Let $x \in S$.

Then:

So $x = x \vee x$.

The result $x = x \wedge x$ follows from Duality Principle (Boolean Algebras).