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Theorem cbvral3v 2845
 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 2656 . . 3
32cbvralv 2835 . 2
4 cbvral3v.2 . . . 4
5 cbvral3v.3 . . . 4
64, 5cbvral2v 2843 . . 3
76ralbii 2638 . 2
83, 7bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wceq 1642  wral 2614 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619 This theorem is referenced by: (None)
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