Integer Multiplication is Associative

Theorem
Integer multiplication is associative:

$$\left({\left[\left[{a, b}\right]\right]_\boxminus \times \left[\left[{c, d}\right]\right]_\boxminus}\right) \times \left[\left[{e, f}\right]\right]_\boxminus = \left[\left[{a, b}\right]\right]_\boxminus \times \left({\left[\left[{c, d}\right]\right]_\boxminus \times \left[\left[{e, f}\right]\right]_\boxminus}\right) $$

Proof
From Natural Numbers form Semiring, we take it for granted that addition and multiplication are commutative and associative on the natural numbers $$\mathbb{N}$$.