B-Algebra Identity: xy=x(0(0y))

Theorem
Let $\left({X, \circ}\right)$ be a $B$-algebra.

Then:


 * $\forall x,y \in X: x \circ y = x \circ\left({0 \circ\left({ 0 \circ y}\right)}\right)$

Proof
Let $x, y \in X$.

Then:

Hence the result.