Mellin Transform of Dirac Delta Function by Function

Theorem
Let $f: \R \to \R$ be a function.

Let $c \in \R_{>0}$ be a positive constant real number.

Let $\delta_c \left({t}\right)$ be the Dirac delta function.

Let $\mathcal M$ be the Mellin transform.

Then:
 * $\mathcal M \left\{ {\delta_c \left({t}\right) f \left({t}\right)} \right\} \left({s}\right) = c^{s - 1} f \left({c}\right)$