Natural Number Addition Commutativity with Successor

Theorem
Let $\N$ be the natural numbers.

Then:
 * $\forall m, n \in \N: m^+ + n = \paren {m + n}^+$

Also defined as
Thus, in the context of 1-based natural numbers, this result can be written:
 * $\forall m, n \in \N_{> 0}: \paren {m + 1} + n = \paren {m + n} + 1$