Exponentiation Functor is Functor

Theorem
Let $\mathbf C$ be a Cartesian closed metacategory.

Let $A$ be an object of $\mathbf C$.

Let $\left({-}\right)^A: \mathbf C \to \mathbf C$ be the exponentiation functor.

Then $\left({-}\right)^A$ is a functor.