Power Structure of Group is Semigroup/Proof 2

Theorem
Let $\left({G, \circ}\right)$ be a group.

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

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

Proof
By definition a group is also a semigroup.

The result then follows from Power Set of Semigroup under Induced Operation is Semigroup.