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Metamath Proof Explorer

Theorem eximdv

Description: Deduction form of Theorem 19.22 of Margaris p. 90, see exim . See eximdh and eximd for versions without a distinct variable condition. (Contributed by NM, 27-Apr-1994)

		Ref	Expression
	Hypothesis	alimdv.1	$⊢ φ \to (ψ \to χ)$
	Assertion	eximdv	$⊢ φ \to (\exists x ψ \to \exists x χ)$

Proof

Step	Hyp	Ref	Expression
1		alimdv.1	$⊢ φ \to (ψ \to χ)$
2		ax-5	$⊢ φ \to \forall x φ$
3	2 1	eximdh	$⊢ φ \to (\exists x ψ \to \exists x χ)$