Ordinal is Member of Class of All Ordinals

Theorem
Let $A$ be an ordinal.

Then:
 * $A \in \operatorname{On} \lor A = \operatorname{On}$

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

Proof
By hypothesis $A$ is an ordinal

From Ordinal Class is Ordinal and Ordinal Membership is Trichotomy:
 * $A \in \operatorname{On} \lor A = \operatorname{On} \lor \operatorname{On} \in A$

But by the Burali-Forti Paradox $\operatorname{On}$ is a proper class.

Therefore:
 * $A \in \operatorname{On} \lor A = \operatorname{On}$