Universality of the uniform distribution

Let $𝑌 \sim U (0, 1)$ , $𝐹$ be the cumulative distribution function of a real random variable $𝑋 : 𝜉 \to ℝ$ , and $𝐹 - 1$ be the corresponding Quantile function. Then prob

𝐹 (𝑋) \sim 𝑌 𝑋 \sim 𝐹 - 1 (𝑌)

Proof

proof