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Theorem cbvral3v 3041
 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 2845 . . 3
32cbvralv 3031 . 2
4 cbvral3v.2 . . . 4
5 cbvral3v.3 . . . 4
64, 5cbvral2v 3039 . . 3
76ralbii 2832 . 2
83, 7bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184  wral 2751 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-5 1723  ax-6 1769  ax-7 1812  ax-10 1859  ax-11 1864  ax-12 1876  ax-13 2024  ax-ext 2378 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-ex 1632  df-nf 1636  df-sb 1762  df-cleq 2392  df-clel 2395  df-nfc 2550  df-ral 2756 This theorem is referenced by:  latdisd  16034
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