Inverse of Group Isomorphism is Isomorphism

Theorem
Let $\struct {G, \circ}$ and $\struct {H, *}$ be groups.

Let $\phi: \struct {G, \circ} \to \struct {H, *}$ be a mapping.

Then $\phi$ is an isomorphism $\phi^{-1}: \struct {H, *} \to \struct {G, \circ}$ is also an isomorphism.