Ordering on Natural Numbers is Trichotomy

Theorem
Let $\N$ be the natural numbers.

Let $<$ be the (strict) ordering on $\N$.

Then exactly one of the following is true:
 * $(1): \quad a = b$
 * $(2): \quad a > b$
 * $(3): \quad a < b$

That is, $<$ is a trichotomy on $\N$.