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Theorem cbvmpt2v 6377
Description: Rule to change the bound variable in a maps-to function, using implicit substitution. With a longer proof analogous to cbvmpt 4542, some distinct variable requirements could be eliminated. (Contributed by NM, 11-Jun-2013.)
Hypotheses
Ref Expression
cbvmpt2v.1
cbvmpt2v.2
Assertion
Ref Expression
cbvmpt2v
Distinct variable groups:   , , , ,   , , , ,   , ,   , ,

Proof of Theorem cbvmpt2v
StepHypRef Expression
1 nfcv 2619 . 2
2 nfcv 2619 . 2
3 nfcv 2619 . 2
4 nfcv 2619 . 2
5 cbvmpt2v.1 . . 3
6 cbvmpt2v.2 . . 3
75, 6sylan9eq 2518 . 2
81, 2, 3, 4, 7cbvmpt2 6376 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  e.cmpt2 6298
This theorem is referenced by:  seqomlem0  7133  dffi3  7911  cantnfsuc  8110  cantnfsucOLD  8140  fin23lem33  8746  om2uzrdg  12067  uzrdgsuci  12071  sadcp1  14105  smupp1  14130  imasvscafn  14934  mgmnsgrpex  16049  sgrpnmndex  16050  sylow1  16623  sylow2b  16643  sylow3lem5  16651  sylow3  16653  efgmval  16730  efgtf  16740  frlmphl  18812  pmatcollpw3lem  19284  mp2pm2mplem3  19309  txbas  20068  bcth  21768  opnmbl  22011  mbfimaopn  22063  mbfi1fseq  22128  motplusg  23929  ttgval  24178  numclwwlk5  25112  opsqrlem3  27061  fvproj  27835  dya2iocival  28244  sxbrsigalem5  28259  sxbrsigalem6  28260  eulerpart  28321  sseqp1  28334  cvmliftlem15  28743  cvmlift2  28761  opnmbllem0  30050  mblfinlem1  30051  mblfinlem2  30052  sdc  30237  funcrngcsetc  32806  funcrngcsetcALT  32807  funcringcsetc  32843  lmod1zr  33094  tendoplcbv  36501  dvhvaddcbv  36816  dvhvscacbv  36825
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-oprab 6300  df-mpt2 6301
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