This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem rexeqOLD

Description: Obsolete version of raleq as of 9-Mar-2025. (Contributed by NM, 29-Oct-1995) Remove usage of ax-10 , ax-11 , and ax-12 . (Revised by Steven Nguyen, 30-Apr-2023) (New usage is discouraged.) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	rexeqOLD	$⊢ A = B \to (\exists x \in A φ \leftrightarrow \exists x \in B φ)$

Proof

Step	Hyp	Ref	Expression
1		biidd	$⊢ A = B \to (φ \leftrightarrow φ)$
2	1	rexeqbi1dv	$⊢ A = B \to (\exists x \in A φ \leftrightarrow \exists x \in B φ)$