Full Idea
In the presence of other axioms, the Axiom of Foundation is equivalent to the claim that every set is a member of some Vα.
Clarification
A Vα is a stage of the hierarchy
Gist of Idea
The Axiom of Foundation says every set exists at a level in the set hierarchy
Source
Penelope Maddy (Naturalism in Mathematics [1997], I.3)
Book Reference
Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.60