Full Idea
Axiom of Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y). That is, a set is determined by its members. If every z in one set is also in the other set, then the two sets are the same.
Gist of Idea
Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y)
Source
Kenneth Kunen (Set Theory [1980], §1.5)
Book Reference
Kunen,Kenneth: 'Set Theory: Introduction to Independence Proofs' [North-Holland 1980], p.10