Don't worry, they work!
You have to understand that these are the "irreducible folds" of origami, so IF THEY ARE POSSIBLE you can just make them without any extra explanation as to how or why they are possible. The last few are to some people unintuitive without a practical demonstration, which is why it is useful to have a list like this.
A person might challenge a folding step which instructs you to fold in a certain way, saying it is inexact or not unique, but then all you need to do is quote the axiom that corrects them.