Image of Group Homomorphism is Subgroup

Theorem
Let $\phi: G_1 \to G_2$ be a group homomorphism.

Then:
 * $\Img \phi \le G_2$

where $\le$ denotes the relation of being a subgroup.

Proof
This is a special case of Group Homomorphism Preserves Subgroups, where we set $H = G_1$.