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Theorem reseq2 4607
 Description: Equality theorem for restrictions. (Contributed by NM, 8-Aug-1994.)
Assertion
Ref Expression
reseq2

Proof of Theorem reseq2
StepHypRef Expression
1 xpeq1 4359 . . 3
21ineq2d 3138 . 2
3 df-res 4357 . 2
4 df-res 4357 . 2
52, 3, 43eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243  cvv 2557   cin 2916   cxp 4343   cres 4347 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-opab 3819  df-xp 4351  df-res 4357 This theorem is referenced by:  reseq2i  4609  reseq2d  4612  resabs1  4640  resima2  4644  imaeq2  4664  resdisj  4751  relcoi1  4849  fressnfv  5350  tfrlem1  5923  tfrlem9  5935  tfr0  5937  tfrlemisucaccv  5939  tfrlemiubacc  5944
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