Invertible Element of Associative Structure is Cancellable/Corollary

Theorem
Let $\struct {S, \circ}$ be a monoid whose identity element is $e_S$.

An element of $\struct {S, \circ}$ which is invertible is also cancellable.

Proof
By definition, a monoid is an associative algebraic structure with an identity element.

The result follows from Invertible Element of Associative Structure is Cancellable.