Induced Group Product is Homomorphism iff Commutative/Corollary

Corollary to Group Abelian iff Induced Group Product is Homomorphism
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
We have that $G$ is a subgroup of itself.

The result then follows from Group Abelian iff Induced Group Product is Homomorphism by putting $H_1 = H_2 = G$.