Theorem rmobidv

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

	Ref	Expression
Hypothesis	rmobidv.1	|- ( ph -> ( ps <-> ch ) )
Assertion	rmobidv	|- ( ph -> ( E* x e. A ps <-> E* x e. A ch ) )

Proof

Step	Hyp	Ref	Expression
1		rmobidv.1	|- ( ph -> ( ps <-> ch ) )
2	1	adantr	|- ( ( ph /\ x e. A ) -> ( ps <-> ch ) )
3	2	rmobidva	|- ( ph -> ( E* x e. A ps <-> E* x e. A ch ) )