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Theorem reseq2i 4968
Description: Equality inference for restrictions. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
reseqi.1  |-  A  =  B
Assertion
Ref Expression
reseq2i  |-  ( C  |`  A )  =  ( C  |`  B )

Proof of Theorem reseq2i
StepHypRef Expression
1 reseqi.1 . 2  |-  A  =  B
2 reseq2 4966 . 2  |-  ( A  =  B  ->  ( C  |`  A )  =  ( C  |`  B ) )
31, 2ax-mp 8 1  |-  ( C  |`  A )  =  ( C  |`  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1632    |` cres 4707
This theorem is referenced by:  reseq12i  4969  rescom  4996  rescnvcnv  5151  resdm2  5179  funcnvres  5337  resasplit  5427  fresaunres2  5429  fresaunres1  5430  resdif  5510  resin  5511  domss2  7036  ordtypelem1  7249  ackbij2lem3  7883  facnn  11306  fac0  11307  ruclem4  12528  setsid  13203  dprd2da  15293  ply1plusgfvi  16336  uptx  17335  txcn  17336  ressxms  18087  ressms  18088  iscmet3lem3  18732  volres  18903  dvlip  19356  dvne0  19374  lhop  19379  dflog2  19934  dfrelog  19939  dvlog  20014  wilthlem2  20323  ghsubgolem  21053  zrdivrng  21115  hashresfn  23189  df1stres  23258  df2ndres  23259  wfrlem5  24331  frrlem5  24356  domrancur1c  25305  empos  25345  dispos  25390  isdrngo1  26690  eldioph4b  26997  diophren  26999  seff  27641  sblpnf  27642  0pth  28356  bnj1326  29372
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-opab 4094  df-xp 4711  df-res 4717
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