Ordinal Number Equivalent to Cardinal Number

Theorem
Let $x$ be an ordinal.

Let $\card x$ denote the cardinal number of $x$.

Then:


 * $x \sim \card x$

where $\sim$ denotes set equivalence.

Proof
From Set is Equivalent to Itself:
 * $x \sim x$

Therefore, $x$ is equivalent to some ordinal.

By Condition for Set Equivalent to Cardinal Number:
 * $x \sim \card x$