Equivalent to the axiom of choice? [duplicate]

Are the two following equivalent under ZF :

1. Axiom of Choice/Zorn's Lemma
2. 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 :)