Ordinal is Subset of Class of All Ordinals

Theorem
Suppose $A$ is an ordinal.

Then:
 * $A \subseteq \operatorname{On}$

where $\operatorname{On}$ represents the class of all ordinals.

Proof
By Ordinal is Member of Ordinal Class:
 * $A \in \operatorname{On} \lor A = \operatorname{On}$.

In either case:
 * $A \subseteq \operatorname{On}$

since $\operatorname{On}$ is transitive.