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Theorem fvmpts 5958
 Description: Value of a function given in maps-to notation, using explicit class substitution. (Contributed by Scott Fenton, 17-Jul-2013.) (Revised by Mario Carneiro, 31-Aug-2015.)
Hypothesis
Ref Expression
fvmpts.1
Assertion
Ref Expression
fvmpts
Distinct variable group:   ,

Proof of Theorem fvmpts
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 3437 . 2
2 fvmpts.1 . . 3
3 nfcv 2619 . . . 4
4 nfcsb1v 3450 . . . 4
5 csbeq1a 3443 . . . 4
63, 4, 5cbvmpt 4542 . . 3
72, 6eqtri 2486 . 2
81, 7fvmptg 5954 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  [_csb 3434  e.cmpt 4510  `cfv 5593 This theorem is referenced by:  fvmptd  5961  fvmpt2curryd  7019  mptnn0fsupp  12103  mptnn0fsuppr  12105  zsum  13540  prodss  13754  fprodser  13756  fprodn0  13783  fprodefsum  13830  pcmpt  14411  issubc  15204  gsummptnn0fz  17014  mptscmfsupp0  17576  gsummoncoe1  18346  fvmptnn04if  19350  prdsdsf  20870  itgparts  22448  dchrisumlema  23673  abfmpeld  27492  abfmpel  27493  aomclem6  31005  ellimcabssub0  31623  constlimc  31630  cdlemk40  36643 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-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  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-uni 4250  df-br 4453  df-opab 4511  df-mpt 4512  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-iota 5556  df-fun 5595  df-fv 5601
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