Isomorphism (Category Theory) is Monic

Theorem
Let $\mathbf C$ be a metacategory.

Let $f: C \to D$ be an isomorphism.

Then $f: C \rightarrowtail D$ is monic.

Proof
Since $f$ is an isomorphism, it is a fortiori a split monomorphism.

The result follows from Split Monomorphism is Monic.