For the record, I had the same feeling initially, but figured out it wasn't really the "if and only if" that was confusing me, but mostly the actual contents of what's being said. (E.g. compare my last answer above.) Do you feel the "if and only if"s in my proposed alternative, i.e.
is confusing you, too?
Actually, I'm just noticing, that the second one of those lacks the "only if" part, so perhaps "must" or "has to" together with "if and only if" did make me (uncouciously) feel uncomfortable after all, and I dropped it.
Note that "if and only if" or "if" is, in practice, often used interchangeably in definitions in maths, as far as I'm aware. (Interchangeable only in definitions, when it's clear from context that it actually means to be a precise definition, and definitely not in theorems!)
I don't feel like that would add any clarity. In any case, I agree that this is not quite relevant when the point is to figure out the actual rules, not the best way to present them.