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

Metamath Proof Explorer

Theorem eximd

Description: Deduction form of Theorem 19.22 of Margaris p. 90, see exim . (Contributed by NM, 29-Jun-1993) (Revised by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypotheses	eximd.1	$⊢ Ⅎ x φ$
	eximd.2	$⊢ φ \to (ψ \to χ)$
Assertion	eximd	$⊢ φ \to (\exists x ψ \to \exists x χ)$

Proof

Step	Hyp	Ref	Expression
1		eximd.1	$⊢ Ⅎ x φ$
2		eximd.2	$⊢ φ \to (ψ \to χ)$
3	1	nf5ri	$⊢ φ \to \forall x φ$
4	3 2	eximdh	$⊢ φ \to (\exists x ψ \to \exists x χ)$