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)

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

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