Natural Number Multiplication is Associative

Theorem
The operation of multiplication on the set of natural numbers $\N$ is associative:


 * $\forall x, y, z \in \N: \left({x \times y}\right) \times z = x \times \left({y \times z}\right)$

Proof 3
In the Axiomatization of 1-Based Natural Numbers, this is rendered:
 * $\forall x, y, z \in \N_{> 0}: \left({x \times y}\right) \times z = x \times \left({y \times z}\right)$