Natural Number Multiplication is Associative/Proof 1

Proof
From Index Laws for Semigroup: Product of Indices we have:


 * $+^{z \times y} x = +^z \left({+^y x}\right)$

By definition of multiplication, this amounts to:


 * $x \times \left({z \times y}\right) = \left({x \times y}\right) \times z$

From Natural Number Multiplication is Commutative, we have:


 * $x \times \left({z \times y}\right) = x \times \left({y \times z}\right)$