Several readers have pointed out a "logic gap" in Problem and Solution 5-8 on page 160 of Math Proofs Demystified.
I recommend that you simply take the statement of Problem 5-8 as an assumption itself, and call it the "AIA axiom."
I hope to correct this problem in future editions (if they ever exist) by carefully rewriting this whole Chapter 5. However, I'd really like to see my publisher find a way to come out with "dynamic books in the cloud," so that errors of this sort could be corrected immediately and for good!
What do you think, dear readers? Would you like to see books like this produced so that you could read them on a tablet device, provide feedback to me (the author), and see changes made, if needed, on the spot?