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Theorem 2ralbidva 2340
Description: Formula-building rule for restricted universal quantifiers (deduction rule). (Contributed by NM, 4-Mar-1997.)
Hypothesis
Ref Expression
2ralbidva.1 ((φ (x A y B)) → (ψχ))
Assertion
Ref Expression
2ralbidva (φ → (x A y B ψx A y B χ))
Distinct variable groups:   x,y,φ   y,A
Allowed substitution hints:   ψ(x,y)   χ(x,y)   A(x)   B(x,y)

Proof of Theorem 2ralbidva
StepHypRef Expression
1 nfv 1418 . 2 xφ
2 nfv 1418 . 2 yφ
3 2ralbidva.1 . 2 ((φ (x A y B)) → (ψχ))
41, 2, 32ralbida 2339 1 (φ → (x A y B ψx A y B χ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98   wcel 1390  wral 2300
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305
This theorem is referenced by:  soinxp  4353  isotr  5399
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