Link diagrams and Reidemeister moves

Question

I am studying Knots on "Algebraic Graph Theory" written by Godsil & Royle. They state the following theorem:

$\underline{Theorem}$ Two link diagrams determine the same link if and only if one can be obtained from the other by a sequence of Reidemeister moves and planar isotopies.

Unfortunately, they don't give a proof because it is "entirely topological". So as I am curious I would like to ask if someone knows a reference for this proof. I thank you for your attention and for the help.

Answer 1

For example, Prasolov and Sossinsky, "Knots, Links, Braids and 3-Manifolds". It's theorem 1.7 on page 11.