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Theorem reli 5675
 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 df-id 5437 . 2 I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
21relopabi 5671 1 Rel I
 Colors of variables: wff setvar class Syntax hints:   I cid 5436  Rel wrel 5537 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-11 2161  ax-12 2178  ax-ext 2794 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-v 3471  df-un 3913  df-in 3915  df-ss 3925  df-sn 4540  df-pr 4542  df-op 4546  df-opab 5105  df-id 5437  df-xp 5538  df-rel 5539 This theorem is referenced by:  ideqg  5699  issetid  5702  iss  5881  intirr  5956  elid  6034  funi  6366  f1ovi  6635  idssen  8541  symgcom2  30759  idsset  33425  bj-ideqgALT  34534  bj-ideqb  34535  bj-ideqg1ALT  34541  bj-opelidb1ALT  34542  bj-elid5  34545  brid  35682  iss2  35719  refrelid  35879  idsymrel  35915  disjALTVid  36103
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