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Metamath Proof Explorer

Theorem rexbidvALT

Description: Alternate proof of rexbidv , shorter but requires more axioms. (Contributed by NM, 20-Nov-1994) (New usage is discouraged.) (Proof modification is discouraged.)

		Ref	Expression
	Hypothesis	rexbidvALT.1	$⊢ φ \to (ψ \leftrightarrow χ)$
	Assertion	rexbidvALT	$⊢ φ \to (\exists x \in A ψ \leftrightarrow \exists x \in A χ)$

Proof

Step	Hyp	Ref	Expression
1		rexbidvALT.1	$⊢ φ \to (ψ \leftrightarrow χ)$
2		nfv	$⊢ Ⅎ x φ$
3	2 1	rexbid	$⊢ φ \to (\exists x \in A ψ \leftrightarrow \exists x \in A χ)$