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Theorem reli 5135
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

Proof of Theorem reli
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfid3 4801 . 2
21relopabi 5133 1
Colors of variables: wff setvar class
Syntax hints:   cid 4795  Relwrel 5009
This theorem is referenced by:  ideqg  5159  issetid  5162  iss  5326  intirr  5390  funi  5623  f1ovi  5857  idssen  7580  idsset  29540  bj-elid  34599
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-id 4800  df-xp 5010  df-rel 5011
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