Theorem rmobidv

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

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

Proof

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