Ordinal Membership is Trichotomy/Corollary

Corollary to Ordinal Membership is Trichotomy
Let $\alpha$ be an ordinal.

Let $x, y \in \alpha$ such that $x \ne y$.

Then either:
 * $x \in y$

or:
 * $y \in x$

Proof
We have that Element of Ordinal is Ordinal.

The result then follows directly from Ordinal Membership is Trichotomy.