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Theorem relopab 4891
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 2358 . 2  |-  { <. x ,  y >.  |  ph }  =  { <. x ,  y >.  |  ph }
21relopabi 4890 1  |-  Rel  { <. x ,  y >.  |  ph }
Colors of variables: wff set class
Syntax hints:   {copab 4155   Rel wrel 4773
This theorem is referenced by:  opabid2  4894  inopab  4895  difopab  4896  dfres2  5081  cnvopab  5162  funopab  5366  relmptopab  6149  elopabi  6269  relmpt2opab  6285  shftfn  11658  isfunc  13831  eqgval  14759  eltopspOLD  16756  lgsquadlem3  20701  relfae  23862  linedegen  25325  opelopab3  25697  prtlem12  26058  dicvalrelN  31427  diclspsn  31436  dih1dimatlem  31571
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-sep 4220  ax-nul 4228  ax-pr 4293
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-ral 2624  df-rex 2625  df-rab 2628  df-v 2866  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-opab 4157  df-xp 4774  df-rel 4775
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