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Are the two following equivalent under ZF :
- Axiom of Choice/Zorn's Lemma
- Given any two sets A, B, there exists an injection from A to B or there exists an injection from B to A
I could prove that (1) implies (2) and I wonder if they are actually equivalent but I couldn't prove it. I read somewhere that (2) cannot be proven with only ZF, that's why the equivalence seems plausible to me.
Thank you :)