Preimage of Mapping equals Domain

Theorem
The preimage of a mapping is the same set as its domain:


 * $\Preimg f = \Dom f$

Proof
Let $f \subseteq S \times T$ be a mapping.

Then:

From Preimage of Relation is Subset of Domain, we have that $\Preimg f \subseteq S$.

The result follows from the definition of set equality.