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Theorem cbvral2v 2665
 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 2437 . . 3
32cbvralv 2654 . 2
4 cbvral2v.2 . . . 4
54cbvralv 2654 . . 3
65ralbii 2441 . 2
73, 6bitri 183 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wral 2416 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421 This theorem is referenced by:  cbvral3v  2667  fununi  5191  fiintim  6817  isoti  6894  cauappcvgprlemlim  7476  caucvgprlemnkj  7481  caucvgprlemcl  7491  caucvgprprlemcbv  7502  axcaucvglemcau  7713  axpre-suploc  7717  seqvalcd  10239  seqovcd  10243  seq3distr  10293  ennnfonelemr  11943  ctinf  11950
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