Natural Number is Ordinal/Proof 1

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Let $n \in \N$ be a natural number.

Then $n$ is an ordinal.


Consider the class of all ordinals $\On$.

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

Hence a fortiori $\On$ 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.