Natural Number Addition Commutativity with Successor

Theorem
Let $\N$ be the natural numbers.

Then:
 * $\forall m, n \in \N: m^+ + n = \left({m + n}\right)^+$

This can alternatively be written in the context of 1-based natural numbers:
 * $\forall m, n \in \N_{> 0}: \left({m + 1}\right) + n = \left({m + n}\right) + 1$