Inclusion Mapping on Subgroup is Monomorphism

Theorem
Let $\left({G, \circ}\right)$ be a group.

Let $\left({H, \circ {\restriction_H}}\right)$ be a subgroup of $G$.

Let $\iota: H \to G$ be the inclusion mapping from $H$ to $G$.

Then $\iota$ is a group monomorphism.

Proof
We have:
 * Inclusion Mapping on Subgroup is Homomorphism


 * Inclusion Mapping is Injection

The result follows by definition of (group) monomorphism.