Group is Cancellable Monoid

Theorem
Let $\struct {G, \circ}$ be a group.

Then $\struct {G, \circ}$ is a cancellable monoid.

Proof
By definition, a group is a priori a monoid.

From Group Operation is Cancellable, $\circ$ is a cancellable operation in $G$.

Hence the result by definition of cancellable monoid.