Transplanting Theorem/Corollary

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

Let $f: S \to S$ be an automorphism on $\struct {S, \circ}$.

Then the transplant of $\circ$ under $f$ is $\circ$ itself.

Proof
From the Transplanting Theorem there exists one and only one operation $\circ$ such that $f: \struct {S, \circ} \to \struct {S, \circ}$ is an automorphism.