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

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

Then:


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

Proof
Let $x \in X$.

Then:

From 0 in B-Algebra is Left Cancellable Element, we conclude:


 * $x = 0 \circ \paren {0 \circ x}$

as desired.