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Theorem reseq2 4822
 Description: Equality theorem for restrictions. (Contributed by NM, 8-Aug-1994.)
Assertion
Ref Expression
reseq2

Proof of Theorem reseq2
StepHypRef Expression
1 xpeq1 4561 . . 3
21ineq2d 3282 . 2
3 df-res 4559 . 2
4 df-res 4559 . 2
52, 3, 43eqtr4g 2198 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1332  cvv 2689   cin 3075   cxp 4545   cres 4549 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-in 3082  df-opab 3998  df-xp 4553  df-res 4559 This theorem is referenced by:  reseq2i  4824  reseq2d  4827  resabs1  4856  resima2  4861  imaeq2  4885  resdisj  4975  relcoi1  5078  fressnfv  5615  tfrlem1  6213  tfrlem9  6224  tfr0dm  6227  tfrlemisucaccv  6230  tfrlemiubacc  6235  tfr1onlemsucaccv  6246  tfr1onlemubacc  6251  tfr1onlemaccex  6253  tfrcllemsucaccv  6259  tfrcllembxssdm  6261  tfrcllemubacc  6264  tfrcllemaccex  6266  tfrcllemres  6267  tfrcldm  6268  fnfi  6833  lmbr2  12423  lmff  12458
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