Integer Addition is Associative/Proof 1

Theorem
The operation of addition on the set of integers $\Z$ is associative:
 * $\forall x, y, z \in \Z: x + \left({y + z}\right) = \left({x + y}\right) + z$

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

From Integers under Addition form Abelian Group, the integers under addition form a group, from which associativity follows a priori.