Power Set is Closed under Symmetric Difference

Theorem
Let $S$ be a set.

Let $\mathcal P \left({S}\right)$ be the power set of $S$.

Then:
 * $\forall A, B \in \mathcal P \left({S}\right): A * B \in \mathcal P \left({S}\right)$

where $A * B$ is the symmetric difference between $A$ and $B$.

Proof
Let $A, B \subseteq S$, i.e. $A, B \in \mathcal P \left({S}\right)$.