Subset of Ordinal implies Cardinal Inequality

Theorem
Let $S$ be a set.

Let $x$ be an ordinal such that $S \subseteq x$.

Then:


 * $ \left|{ S }\right| \le \left|{ x }\right|$

Proof
Since $x$ is an ordinal, it follows that $x \sim \left|{ x }\right|$ by Ordinal Number Equivalent to Cardinal Number.

This satisfies the hypothesis for Subset implies Cardinal Inequality.

Therefore, $\left|{ S }\right| \le \left|{ x }\right|$.