Integer Addition is Commutative

Theorem
Integer addition is commutative:

$$\left[\left[{a, b}\right]\right]_\boxminus + \left[\left[{c, d}\right]\right]_\boxminus = \left[\left[{c, d}\right]\right]_\boxminus + \left[\left[{a, b}\right]\right]_\boxminus$$

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