Cardinal Number Less than Ordinal/Corollary

Corollary to Cardinal Number Less than Ordinal
Let $x$ be an ordinal.

Let $\left|{x}\right|$ denote the cardinal number of $x$.

Then:


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

Proof
By Set Equivalence is Equivalence Relation:
 * $x \sim x$

By Cardinal Number Less than Ordinal:
 * $\left|{x}\right| \le x$