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Theorem reli 5076
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 4746 . 2  |-  _I  =  { <. x ,  y
>.  |  x  =  y }
21relopabi 5074 1  |-  Rel  _I
Colors of variables: wff setvar class
Syntax hints:    _I cid 4740   Rel wrel 4954
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4522  ax-nul 4530  ax-pr 4640
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3747  df-if 3901  df-sn 3987  df-pr 3989  df-op 3993  df-opab 4460  df-id 4745  df-xp 4955  df-rel 4956
This theorem is referenced by:  ideqg  5100  issetid  5103  iss  5263  intirr  5325  funi  5557  f1ovi  5786  idssen  7465  idsset  28066  bj-elid  32859
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