structural:summarization, structural:scholar_edition
Formal statement

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

or in words:

The converse of this axiom, ∀ A ∀ B (A = B ⟹ ∀ X (X ∈ A ⟺ X ∈ B)), {\displaystyle \forall A\,\forall B\,(A=B\implies \forall X\,(X\in A\iff X\in B)),} follows from the substitution property of equality.