I can think of the "Universality of the Uniform":
Given an Unif(0,1) r.v., we can construct an r.v. with any cts distribution we want. Conversely, given an r.v. with an arbitrary cts distribution, we can create a Unif(0,1). ----From Introduction to Probability by J.K.Blitzstein & J.Hwang.
Other than this "Universality of the Uniform" or "Fundamental theorem of Simulation", is there any other (potentially in more depth) explanation?
Thanks in advance.