Theorem reximddv

Description: Deduction from Theorem 19.22 of Margaris p. 90. (Contributed by Thierry Arnoux, 7-Dec-2016)

	Ref	Expression
Hypotheses	reximddva.1	$$⊢\left(\phi \wedge \left(x\in A\wedge \psi \right)\right)\to \chi$$
	reximddva.2	$$⊢\phi \to \exists x\in A\psi$$
Assertion	reximddv	$$⊢\phi \to \exists x\in A\chi$$

Proof

Step	Hyp	Ref	Expression
1		reximddva.1	$$⊢\left(\phi \wedge \left(x\in A\wedge \psi \right)\right)\to \chi$$
2		reximddva.2	$$⊢\phi \to \exists x\in A\psi$$
3	1	expr	$$⊢\left(\phi \wedge x\in A\right)\to \left(\psi \to \chi \right)$$
4	3	reximdva	$$⊢\phi \to \left(\exists x\in A\psi \to \exists x\in A\chi \right)$$
5	2 4	mpd	$$⊢\phi \to \exists x\in A\chi$$