Class of All Cardinals Contains Minimally Inductive Set

Theorem
Let $\mathcal N$ denote the class of all cardinal numbers.

Then:


 * $\omega \subseteq \mathcal N$

Where $\omega$ denotes the minimal infinite successor set.

Proof
Suppose $n \in \omega$.

By Cardinal of Finite Ordinal, $n = \left|{ n }\right|$.

By Cardinal of Cardinal Equal to Cardinal/Corollary, $n \in \mathcal N$.