Natural Number is Ordinal/Proof 1

Proof
Consider the class of all ordinals $\On$.

From Class of All Ordinals is Minimally Superinductive over Successor Mapping, $\On$ is superinductive.

Hence $\On$ is inductive.

From the von Neumann construction of the natural numbers, $\N$ is identified with the minimally inductive set $\omega$.

By definition of minimally inductive set:
 * $\omega \subseteq \On$

and the result follows.