Theorem elequ2g

Description: A form of elequ2 with a universal quantifier. Its converse is the axiom of extensionality ax-ext . (Contributed by BJ, 3-Oct-2019)

	Ref	Expression
Assertion	elequ2g	$$⊢x=y\to \forall z\left(z\in x\leftrightarrow z\in y\right)$$

Proof

Step	Hyp	Ref	Expression
1		elequ2	$$⊢x=y\to \left(z\in x\leftrightarrow z\in y\right)$$
2	1	alrimiv	$$⊢x=y\to \forall z\left(z\in x\leftrightarrow z\in y\right)$$