Induced Group Product is Homomorphism iff Commutative/Corollary

Corollary to Induced Group Product is Homomorphism iff Commutative
Let $\left({G, \circ}\right)$ be a group.

Let $\phi: G \times G \to G$ be defined such that:
 * $\forall a, b \in G: \phi \left({\left({a, b}\right)}\right) = a \circ b$

Then $\phi$ is a homomorphism iff $G$ is abelian.

Proof
$G$ is a Subgroup of Itself.

The result then follows from Induced Group Product is Homomorphism iff Commutative by replace $H_1$ and $H_2$ with $G$.