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

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

Then:


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

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

Then:

Hence the result.

Also see
This identity is comparable to Axiom $(A3)$ for $B$-algebras.