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used by Zermelo was "Bestimmtheit". The specific English term "extensionality" only became common in mathematical and logical texts in the 1920s and 1930s, particularly with the formalization of logic and set theory by figures like Alfred Tarski and John von Neumann.

In ZF set theory

In the formal language of the Zermelo-Fraenkel axioms, the axiom reads:

:

or in words:
:If the sets

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