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

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


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

Proof
Let $x \in X$:

From $B$-Algebra Identity: $0 \circ x = 0 \circ y \implies x = y$, we have:


 * $x=0\circ \left({0 \circ x}\right)$

As desired.