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Theorem cbvral3v 2942
 Description: Change bound variables of triple restricted universal quantification, using implicit substitution. (Contributed by NM, 10-May-2005.)
Hypotheses
Ref Expression
cbvral3v.1
cbvral3v.2
cbvral3v.3
Assertion
Ref Expression
cbvral3v
Distinct variable groups:   ,   ,   ,   ,   ,,   ,   ,   ,,   ,,   ,   ,,,   ,,   ,,   ,
Allowed substitution hints:   (,,,,)   (,,,,)   (,,,)   (,,,)   (,,,)   (,)

Proof of Theorem cbvral3v
StepHypRef Expression
1 cbvral3v.1 . . . 4
212ralbidv 2747 . . 3
32cbvralv 2932 . 2
4 cbvral3v.2 . . . 4
5 cbvral3v.3 . . . 4
64, 5cbvral2v 2940 . . 3
76ralbii 2729 . 2
83, 7bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wral 2705 This theorem is referenced by:  latdisd  14616 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710
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