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Metamath Proof Explorer

Theorem rexlimdva

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by NM, 20-Jan-2007)

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

Step	Hyp	Ref	Expression
1		rexlimdva.1	$⊢ (φ \land x \in A) \to (ψ \to χ)$
2	1	ex	$⊢ φ \to (x \in A \to (ψ \to χ))$
3	2	rexlimdv	$⊢ φ \to (\exists x \in A ψ \to χ)$