Laplace Transform of Dirac Delta Function by Function

Theorem
Let $f \left({t}\right): \R \to \R$ or $\R \to \C$ be a function.

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

Let $c$ be a positive constant real number.

Let $\mathcal L \left\{{f \left({t}\right)}\right\} \left({s}\right) = F \left({s}\right)$ be the Laplace Transform of $f$.

Then:
 * $\mathcal L \left\{{\delta \left({t - c}\right) f \left({t}\right)}\right\} \left({s}\right) = e^{- s c} f \left({c}\right)$