Right Cancellable Commutative Operation is Left Cancellable

Theorem
Let $\left({S, \circ}\right)$ be an algebraic structure.

Let $\circ$ be right cancellable and also commutative.

Then $\circ$ is also right cancellable.

Proof
Let $\circ$ be both right cancellable and commutative on a set $S$.

Then:

Also see

 * Left Cancellable Commutative Operation is Right Cancellable