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Theorem relopab 4812
Description: A class of ordered pairs is a relation. (Contributed by NM, 8-Mar-1995.) (Unnecessary distinct variable restrictions were removed by Alan Sare, 9-Jul-2013.) (Proof shortened by Mario Carneiro, 21-Dec-2013.)
Assertion
Ref Expression
relopab  |-  Rel  { <. x ,  y >.  |  ph }

Proof of Theorem relopab
StepHypRef Expression
1 eqid 2283 . 2  |-  { <. x ,  y >.  |  ph }  =  { <. x ,  y >.  |  ph }
21relopabi 4811 1  |-  Rel  { <. x ,  y >.  |  ph }
Colors of variables: wff set class
Syntax hints:   {copab 4076   Rel wrel 4694
This theorem is referenced by:  opabid2  4815  inopab  4816  difopab  4817  dfres2  5002  cnvopab  5083  funopab  5287  relmptopab  6065  elopabi  6185  relmpt2opab  6201  shftfn  11568  isfunc  13738  eqgval  14666  eltopspOLD  16656  lgsquadlem3  20595  linedegen  24766  bosser  26167  opelopab3  26373  prtlem12  26735  dicvalrelN  31375  diclspsn  31384  dih1dimatlem  31519
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-opab 4078  df-xp 4695  df-rel 4696
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