Class of Cardinals Contains Minimal Infinite Successor Set

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

Then:


 * $\omega \subseteq \NN$

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

Proof
Suppose $n \in \omega$.

By Cardinal of Finite Ordinal, $n = \card n$.

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