Symmetric Group is Group/Proof 2

Theorem

Let $S$ be a set.

Let $\map \Gamma S$ denote the set of all permutations on $S$.

Then $\struct {\map \Gamma S, \circ}$, the symmetric group on $S$, forms a group.

Proof

A direct application of Set of Invertible Mappings forms Symmetric Group.

$\blacksquare$