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Theorem cbvmpt2 6376
Description: Rule to change the bound variable in a maps-to function, using implicit substitution. (Contributed by NM, 17-Dec-2013.)
Hypotheses
Ref Expression
cbvmpt2.1
cbvmpt2.2
cbvmpt2.3
cbvmpt2.4
cbvmpt2.5
Assertion
Ref Expression
cbvmpt2
Distinct variable groups:   , , , ,   , , , ,

Proof of Theorem cbvmpt2
StepHypRef Expression
1 nfcv 2619 . 2
2 nfcv 2619 . 2
3 cbvmpt2.1 . 2
4 cbvmpt2.2 . 2
5 cbvmpt2.3 . 2
6 cbvmpt2.4 . 2
7 eqidd 2458 . 2
8 cbvmpt2.5 . 2
91, 2, 3, 4, 5, 6, 7, 8cbvmpt2x 6375 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  F/_wnfc 2605  e.cmpt2 6298
This theorem is referenced by:  cbvmpt2v  6377  fnmpt2ovd  6878  fmpt2co  6883  mpt2curryd  7017  fvmpt2curryd  7019  xpf1o  7699  cnfcomlem  8164  cnfcomlemOLD  8172  fseqenlem1  8426  gsumdixpOLD  17257  gsumdixp  17258  evlslem4OLD  18173  evlslem4  18174  madugsum  19145  cnmpt2t  20174  cnmptk2  20187  fmucnd  20795  fsum2cn  21375  relexpsucr  29053  fmuldfeqlem1  31576
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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