Theorem rmobidva

Description: Formula-building rule for restricted existential quantifier (deduction form). (Contributed by NM, 16-Jun-2017)

	Ref	Expression
Hypothesis	rmobidva.1	$$⊢\left(\phi \wedge x\in A\right)\to \left(\psi \leftrightarrow \chi \right)$$
Assertion	rmobidva	$$⊢\phi \to \left({\exists }^{*}x\in A\psi \leftrightarrow {\exists }^{*}x\in A\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		rmobidva.1	$$⊢\left(\phi \wedge x\in A\right)\to \left(\psi \leftrightarrow \chi \right)$$
2		nfv	$$⊢Ⅎx\phi$$
3	2 1	rmobida	$$⊢\phi \to \left({\exists }^{*}x\in A\psi \leftrightarrow {\exists }^{*}x\in A\chi \right)$$