Image under Inclusion Mapping

Theorem
Let $X$ be a set.

Let $S \subseteq X$, $Z \subseteq S$.

Then $i_S\left[{Z}\right] = Z$

where
 * $i_S$ denotes the inclusion mapping of $S$,
 * $i_S\left[{Z}\right]$ denotes the image of $Z$ under $i_S$.

Proof
Thus