Can someone explain their ideas of solving this question? I have the hint of this question, but still confused. What does R' mean here? Please explain how to prove this statement in details. No need to prove it for me, just explain the process of thinking is okay!

Question:

\fProve that the set of real numbers as defined by axioms 1 to 13 is unique in the following sense: If R' is a set which satisfies axioms 1 to 13, there exists a one-to-one function f from R onto R' which satisfies fx + >) = f() +/() for all x, VER for all x, ye R f(x) for x, YER