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Theorem reli 5060
Description: The identity relation is a relation. Part of Exercise 4.12(p) of [Mendelson] p. 235. (Contributed by NM, 26-Apr-1998.) (Revised by Mario Carneiro, 21-Dec-2013.)
Assertion
Ref Expression
reli  |-  Rel  _I

Proof of Theorem reli
Dummy variables  x  y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfid3 4727 . 2  |-  _I  =  { <. x ,  y
>.  |  x  =  y }
21relopabi 5057 1  |-  Rel  _I
Colors of variables: wff setvar class
Syntax hints:    _I cid 4721   Rel wrel 4935
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1633  ax-4 1646  ax-5 1719  ax-6 1765  ax-7 1808  ax-9 1840  ax-10 1855  ax-11 1860  ax-12 1872  ax-13 2020  ax-ext 2374  ax-sep 4505  ax-nul 4513  ax-pr 4618
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1402  df-ex 1628  df-nf 1632  df-sb 1758  df-clab 2382  df-cleq 2388  df-clel 2391  df-nfc 2546  df-ne 2593  df-ral 2751  df-rex 2752  df-rab 2755  df-v 3053  df-dif 3409  df-un 3411  df-in 3413  df-ss 3420  df-nul 3729  df-if 3875  df-sn 3962  df-pr 3964  df-op 3968  df-opab 4443  df-id 4726  df-xp 4936  df-rel 4937
This theorem is referenced by:  ideqg  5084  issetid  5087  iss  5250  intirr  5315  funi  5543  f1ovi  5777  idssen  7501  idsset  29733  bj-elid  34986
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