Group Homomorphism Preserves Identity/Proof 1

Theorem
Let $\left({G, \circ}\right)$ and $\left({H, *}\right)$ be groups.

Let $\phi: \left({G, \circ}\right) \to \left({H, *}\right)$ be a group homomorphism.

Let:
 * $e_G$ be the identity of $G$
 * $e_H$ be the identity of $H$.

Then:
 * $\phi \left({e_G}\right) = e_H$

Proof
That is: