Cayley's Representation Theorem/Proof 1

Proof
Let $H = \left\{{e}\right\}$.

We can apply Permutation of Cosets to $H$ so that:
 * $\mathbb S = G$

and:
 * $\ker \left({\theta}\right) = \left\{{e}\right\}$

The result follows by the First Isomorphism Theorem.