Full Idea
The Axiom of Extensionality says that for all sets x and y, if x and y have the same elements then x = y.
Gist of Idea
Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
Book Reference
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.50
A Reaction
This seems fine in pure set theory, but hits the problem of renates and cordates in the real world. The elements coincide, but the axiom can't tell you why they coincide.