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Theorem cbvral2v 2541
 Description: Change bound variables of double restricted universal quantification, using implicit substitution. (Contributed by NM, 10-Aug-2004.)
Hypotheses
Ref Expression
cbvral2v.1
cbvral2v.2
Assertion
Ref Expression
cbvral2v
Distinct variable groups:   ,   ,   ,,   ,,   ,   ,   ,   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,)   (,)

Proof of Theorem cbvral2v
StepHypRef Expression
1 cbvral2v.1 . . . 4
21ralbidv 2326 . . 3
32cbvralv 2533 . 2
4 cbvral2v.2 . . . 4
54cbvralv 2533 . . 3
65ralbii 2330 . 2
73, 6bitri 173 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wral 2306 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311 This theorem is referenced by:  cbvral3v  2543  fununi  4967  cauappcvgprlemlim  6759  caucvgprlemnkj  6764  caucvgprlemcl  6774  caucvgprprlemcbv  6785  axcaucvglemcau  6972  iseqdistr  9249
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