Commutative B-Algebra Implies (zy)(zx)=xy

Theorem
Let $\struct {B, \circ}$ be a commutative $B$-algebra.

Then:
 * $\forall x, y, z \in X: \paren {z \circ y} \circ \paren {z \circ x} = x \circ y$

Proof
Let $x, y, z \in X$.

Then: