# 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 $H = G_1$.

$\blacksquare$