Identity of Monoid is Unique

Theorem
Let $\left({S, \circ}\right)$ be a monoid.

Then $S$ has a unique identity.

Proof
As $\left({S, \circ}\right)$ is an algebraic structure, the result Identity is Unique can be applied directly.

Also see

 * Inverse in Monoid is Unique
 * Identity of Group is Unique