Inverse of Group Isomorphism is Isomorphism

Theorem
Let $\left({G, \circ}\right)$ and $\left({H, *}\right)$ be groups.

Let $\phi: \left({G, \circ}\right) \to \left({H, *}\right)$ be a mapping.

Then $\phi$ is an isomorphism iff $\phi^{-1}: \left({T, *}\right) \to \left({S, \circ}\right)$ is also an isomorphism.