Ordinal is Subset of Class of All Ordinals

Theorem
Suppose $A$ is an ordinal.

Then:
 * $A \subseteq \On$

where $\On$ represents the class of all ordinals.

Proof
By Ordinal is Member of Class of All Ordinals:
 * $A \in \On \lor A = \On$

In either case:
 * $A \subseteq \On$

since $\On$ is transitive.