Theorem reximddv3

Description: Deduction from Theorem 19.22 of Margaris p. 90. (Contributed by Glauco Siliprandi, 5-Feb-2022)

	Ref	Expression
Hypotheses	reximddv3.1	$$⊢\left(\left(\phi \wedge x\in A\right)\wedge \psi \right)\to \chi$$
	reximddv3.2	$$⊢\phi \to \exists x\in A\psi$$
Assertion	reximddv3	$$⊢\phi \to \exists x\in A\chi$$

Proof

Step	Hyp	Ref	Expression
1		reximddv3.1	$$⊢\left(\left(\phi \wedge x\in A\right)\wedge \psi \right)\to \chi$$
2		reximddv3.2	$$⊢\phi \to \exists x\in A\psi$$
3	1	anasss	$$⊢\left(\phi \wedge \left(x\in A\wedge \psi \right)\right)\to \chi$$
4	3 2	reximddv	$$⊢\phi \to \exists x\in A\chi$$