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	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	reximdv	$$⊢\phi \to \left(\exists x\in A\psi \to \exists x\in A\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		ralimdv.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2	1	a1d	$$⊢\phi \to \left(x\in A\to \left(\psi \to \chi \right)\right)$$
3	2	reximdvai	$$⊢\phi \to \left(\exists x\in A\psi \to \exists x\in A\chi \right)$$