Power Structure of Magma is Magma

Theorem
Let $\left({S, \circ}\right)$ be a magma.

Let $\left({\mathcal P \left({S}\right), \circ_\mathcal P}\right)$ be the algebraic structure consisting of the power set of $S$ and the operation induced on $\mathcal P \left({S}\right)$ by $\circ$.

Then $\left({\mathcal P \left({S}\right), \circ_\mathcal P}\right)$ is a magma.

Proof
Let $\left({S, \circ}\right)$ be a magma.

Let $A, B \subseteq S$.

Thus $\left({\mathcal P \left({S}\right), \circ_\mathcal P}\right)$ is a magma.