Direct Image Mapping of Surjection is Surjection

Theorem
Let $f: S \to T$ be a surjection.

Then the mapping induced by $f$ on $\mathcal P \left({S}\right)$:
 * $f^\to: \mathcal P \left({S}\right) \to \mathcal P \left({T}\right)$

is a surjection.