Power Structure of Group is Semigroup/Proof 2

Theorem

Let $\struct {G, \circ}$ be a group.

Let $\struct {\powerset G, \circ_\PP}$ be the power structure of $\struct {G, \circ}$.

Then $\struct {\powerset G, \circ_\PP}$ is a semigroup.

Proof

By definition a group is also a semigroup.

The result then follows from Power Structure of Semigroup is Semigroup.

$\blacksquare$