Theorem ralbidva

Description: Formula-building rule for restricted universal quantifier (deduction form). (Contributed by NM, 4-Mar-1997) Reduce dependencies on axioms. (Revised by Wolf Lammen, 29-Dec-2019)

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

Proof

Step	Hyp	Ref	Expression
1		ralbidva.1	|- ( ( ph /\ x e. A ) -> ( ps <-> ch ) )
2	1	pm5.74da	|- ( ph -> ( ( x e. A -> ps ) <-> ( x e. A -> ch ) ) )
3	2	ralbidv2	|- ( ph -> ( A. x e. A ps <-> A. x e. A ch ) )