I'm new to set theory and ordinals and such things and currently have a question.
I have a proposition which says that the axiom of choice is equivalent to this: "the power set of every well-ordered set is well-ordered."
It's trivial that the statement is true by well-ordering (which is equivalent to axiom of choice). but I can't find the proof in the opposite way. I also have a proof which I can't understand. It seems that the author tried to prove well-ordering (for any sets) using the mentioned statement. but I can't get it.
Note that I need to prove well-ordering using the mentioned statement not proving the statement with or without AC!
This is the proof: Click here
