Laplace Transform of Dirac Delta Function by Function

Theorem
Let $\map f t: \R \to \R$ or $\R \to \C$ be a function.

Let $\map \delta t$ denote the Dirac delta function.

Let $c$ be a positive constant real number.

Let $\laptrans {\map f t} = \map F s$ denote the Laplace transform of $f$.

Then:
 * $\laptrans {\map \delta {t - c} \map f t} = e^{- s c} \map f c$