Structure Induced by Commutative Operation is Commutative

Theorem
Let $\left({T, \circ}\right)$ be an algebraic structure, and let $S$ be a set.

Let $\left({T^S, \oplus}\right)$ be the structure on $T^S$ induced by $\circ$.

If $\circ$ is commutative, then the operation $\oplus$ induced on $T^S$ by $\circ$ is also commutative.

Proof
Let $\left({T, \circ}\right)$ be a commutative algebraic structure.

Let $f, g \in T^S$.

Then: