Theorem ralbidv

Description: Formula-building rule for restricted universal quantifier (deduction form). (Contributed by NM, 20-Nov-1994) Reduce dependencies on axioms. (Revised by Wolf Lammen, 5-Dec-2019)

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