Natural Number Addition is Commutative

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


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

Proof 3
In the axiomatisation of $1$-based natural numbers, this is rendered:
 * $\forall x, y \in \N_{> 0}: x + y = y + x$