Product of Conjugates equals Conjugate of Products

Theorem
Let $\left({G, \circ}\right)$ be a group.

Then:
 * $\forall a, x, y \in G: \left({a \circ x \circ a^{-1}}\right) \circ \left({a \circ y \circ a^{-1}}\right) = a \circ \left({x \circ y}\right) \circ a^{-1}$

That is, the product of conjugates is equal to the conjugate of the product.

Proof
Follows directly from the group axioms.