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Theorem resoprab 6398
 Description: Restriction of an operation class abstraction. (Contributed by NM, 10-Feb-2007.)
Assertion
Ref Expression
resoprab
Distinct variable groups:   ,,,   ,,,

Proof of Theorem resoprab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 resopab 5325 . . 3
2 19.42vv 1777 . . . . 5
3 an12 797 . . . . . . 7
4 eleq1 2529 . . . . . . . . . 10
5 opelxp 5034 . . . . . . . . . 10
64, 5syl6bb 261 . . . . . . . . 9
76anbi1d 704 . . . . . . . 8
87pm5.32i 637 . . . . . . 7
93, 8bitri 249 . . . . . 6
1092exbii 1668 . . . . 5
112, 10bitr3i 251 . . . 4
1211opabbii 4516 . . 3
131, 12eqtri 2486 . 2
14 dfoprab2 6343 . . 3
1514reseq1i 5274 . 2
16 dfoprab2 6343 . 2
1713, 15, 163eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  <.cop 4035  {copab 4509  X.cxp 5002  |cres 5006  {`coprab 6297 This theorem is referenced by:  resoprab2  6399  df1stres  27522  df2ndres  27523 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-ral 2812  df-rex 2813  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-xp 5010  df-rel 5011  df-res 5016  df-oprab 6300
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