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	$$⊢Ⅎx\phi$$
	eximd.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	eximd	$$⊢\phi \to \left(\exists x\psi \to \exists x\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		eximd.1	$$⊢Ⅎx\phi$$
2		eximd.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
3	1	nf5ri	$$⊢\phi \to \forall x\phi$$
4	3 2	eximdh	$$⊢\phi \to \left(\exists x\psi \to \exists x\chi \right)$$