Equivalent Sets have Equal Cardinal Numbers

Theorem
Let $S$ and $T$ be sets.

Let $\vert S \vert$ denote the cardinal number of $S$.

Then:


 * $S \sim T \implies \left\vert{S}\right\vert = \left\vert{T}\right\vert$

Proof
Let $x$ be an arbitrary set that is an ordinal: