Integer Addition is Commutative/Proof 1

Theorem
The operation of addition on the set of integers $\Z$ is commutative:


 * $\forall x, y \in \Z: x + y = y + x$

Proof
From the formal definition of integers, $\left[\!\left[{a, b}\right]\!\right]$ is an equivalence class of ordered pairs of natural numbers.

It can be taken directly from Additive Group of Integers‎ that the integers under addition form an abelian group, from which commutativity follows a priori.