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Metamath Proof Explorer

Theorem reximdv

Description: Deduction from Theorem 19.22 of Margaris p. 90. (Restricted quantifier version with strong hypothesis.) (Contributed by NM, 24-Jun-1998)

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

Proof

Step	Hyp	Ref	Expression
1		ralimdv.1	$⊢ φ \to (ψ \to χ)$
2	1	a1d	$⊢ φ \to (x \in A \to (ψ \to χ))$
3	2	reximdvai	$⊢ φ \to (\exists x \in A ψ \to \exists x \in A χ)$