Theorem rmobidva

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

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

Proof

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