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Theorem 2ralbidv 2322
Description: Formula-building rule for restricted universal quantifiers (deduction rule). (Contributed by NM, 28-Jan-2006.) (Revised by Szymon Jaroszewicz, 16-Mar-2007.)
Hypothesis
Ref Expression
2ralbidv.1 (φ → (ψχ))
Assertion
Ref Expression
2ralbidv (φ → (x A y B ψx A y B χ))
Distinct variable groups:   φ,x   φ,y
Allowed substitution hints:   ψ(x,y)   χ(x,y)   A(x,y)   B(x,y)

Proof of Theorem 2ralbidv
StepHypRef Expression
1 2ralbidv.1 . . 3 (φ → (ψχ))
21ralbidv 2300 . 2 (φ → (y B ψy B χ))
32ralbidv 2300 1 (φ → (x A y B ψx A y B χ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wral 2280
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 1312  ax-gen 1314  ax-4 1377  ax-17 1396
This theorem depends on definitions:  df-bi 110  df-nf 1326  df-ral 2285
This theorem is referenced by:  cbvral3v  2517  poeq1  4006  soeq1  4022  isoeq1  5362  isoeq2  5363  isoeq3  5364  smoeq  5823  elinp  6322
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