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

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

Then:


 * $\forall x, y \in X: x \circ y = x \circ \paren {0 \circ \paren {0 \circ y} }$

Proof
Let $x, y \in X$.

Then:

Hence the result.