Natural Number Addition is Associative

Theorem
The operation of addition on the set of natural numbers $\N$ is associative:


 * $\forall x, y, z \in \N: x + \left({y + z}\right) = \left({x + y}\right) + z$

Proof 3
In the Axiomatization of 1-Based Natural Numbers, this is rendered:
 * $\forall x, y, z \in \N_{> 0}: x + \left({y + z}\right) = \left({x + y}\right) + z$