Inverse of Group Isomorphism is Isomorphism/Proof 1
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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 if and only if $\phi^{-1}: \struct {H, *} \to \struct {G, \circ}$ is also an isomorphism.
Proof
A specific instance of Inverse of Algebraic Structure Isomorphism is Isomorphism.
$\blacksquare$