Non-Zero Natural Numbers under Addition form Semigroup

Theorem
Let $\N_{>0}$ be the set of natural numbers without zero, that is:
 * $\N_{>0} = \N \setminus \set 0$

Let $+$ denote natural number addition.

The structure $\struct {\N_{>0}, +}$ forms a semigroup.

Proof
This is a specific instance of Natural Numbers Bounded Below under Addition form Commutative Semigroup.