Zorn's lemma
Zorn's lemma is equivalent to the well-ordering theorem and also to the axiom of choice, in the sense that any one of the three, together with the Zermelo–Fraenkel axioms of set theory, is sufficient to prove the other two. An earlier formulation of Zorn's lemma is Hausdorff's maximum principle which states that every totally ordered subset of a given partially ordered set is contained in a maximal totally ordered subset of that partially ordered set.