Image of Group Homomorphism is Subgroup

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

Then $$\operatorname{Im} \left({\phi}\right) \le G_2$$.

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