What is "axiom of extensionality"

n. (context set theory English) One of the axioms in axiomatic set theory, equivalent to the statement that two sets are equal if and only if they contain the same elements.

In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo–Fraenkel set theory.