Axiom of Purity
The Axiom of Purity is a possible axiom of material set theory included in most axiomatizations of ZF: set
which is to say, the domain of discourse is restricted to sets,
and thus every set is a pure set and there are no urelements.
Usually, purity is not taken as an axiom and instead everything in the universe is implicitly taken to be a set, doing away with the sethood predicate