Left Distributive and Commutative implies Distributive

Theorem
Let $\struct {S, \circ, *}$ be an algebraic structure.

Let the operation $\circ$ be left distributive over the operation $*$.

Let $\circ$ be commutative.

Then $\circ$ is distributive over $*$.

Proof
Let $a, b, c \in S$.

Then

So $\circ$ is right distributive over $*$.

Since $\circ$ is both left distributive and right distributive over $*$, it is distributive over $*$.