Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that

(i)	$F : \mathbb{R} \to [0, 1]$ is a D205: Probability distribution function for $X$
(ii)	$F$ is an D3393: Invertible function with an D4024: Inverse function $F^{-1} : [0, 1] \to \mathbb{R}$

Let $U \overset{d}{=} \text{Uniform}[0, 1]$ be a D4624: Standard unsigned uniform random real number.

Then \begin{equation} F^{-1}(U) \overset{d}{=} X \end{equation}