Theorem rexbidv

Description: Formula-building rule for restricted existential quantifier (deduction form). (Contributed by NM, 20-Nov-1994) Reduce dependencies on axioms. (Revised by Wolf Lammen, 6-Dec-2019)

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

Proof

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