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Theorem cbvral3v 2639
 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 2434 . . 3
32cbvralv 2629 . 2
4 cbvral3v.2 . . . 4
5 cbvral3v.3 . . . 4
64, 5cbvral2v 2637 . . 3
76ralbii 2416 . 2
83, 7bitri 183 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wral 2391 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396 This theorem is referenced by: (None)
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