Successor Set of Ordinal is Ordinal/Proof 1

Proof
We have the result that Class of All Ordinals is Minimally Superinductive over Successor Mapping.

Hence $\On$ is a superinductive class  the successor mapping.

Hence, by definition of superinductive class:
 * $\On$ is closed under the successor mapping.

That is:
 * $\forall \alpha \in \On: \alpha^+ \in \On$