Theorem bi2raldva 1233

Description: Formula-building rule for restricted universal quantifier (deduction rule).

Hypothesis

Ref	Expression
bi2raldva.1	|- ((ph /\ (x e. A /\ y e. B)) -> (ps <-> ch))

Assertion

Ref	Expression
bi2raldva	|- (ph -> (A.x e. A A.y e. B ps <-> A.x e. A A.y e. B ch))

Distinct variable group(s):   x,y,ph   y,A

Proof of Theorem bi2raldva

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 |- (ph -> A.xph)
2		ax-17 925	. 2 |- (ph -> A.yph)
3		bi2raldva.1	. 2 |- ((ph /\ (x e. A /\ y e. B)) -> (ps <-> ch))
4	1, 2, 3	bi2ralda 1232	1 |- (ph -> (A.x e. A A.y e. B ps <-> A.x e. A A.y e. B ch))

Syntax hints:   -> wi 2   <-> wb 127   /\ wa 196   e. wcel 1092  A.wral 1201

This theorem is referenced by:  f1oweOLD 2944

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677  ax-17 925

This theorem depends on definitions:  df-bi 128  df-an 198  df-ral 1205

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