Theorem exlimdv

Description: Deduction form of Theorem 19.23 of Margaris p. 90, see 19.23 . (Contributed by NM, 27-Apr-1994) Remove dependencies on ax-6 , ax-7 . (Revised by Wolf Lammen, 4-Dec-2017)

	Ref	Expression
Hypothesis	exlimdv.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	exlimdv	$$⊢\phi \to \left(\exists x\psi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		exlimdv.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2	1	eximdv	$$⊢\phi \to \left(\exists x\psi \to \exists x\chi \right)$$
3		ax5e	$$⊢\exists x\chi \to \chi$$
4	2 3	syl6	$$⊢\phi \to \left(\exists x\psi \to \chi \right)$$