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Theorem reli 5787
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 5536 . 2 I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
21relopabiv 5781 1 Rel I
Colors of variables: wff setvar class
Syntax hints:   I cid 5535  Rel wrel 5643
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-v 3450  df-in 3922  df-ss 3932  df-opab 5173  df-id 5536  df-xp 5644  df-rel 5645
This theorem is referenced by:  ideqg  5812  issetid  5815  iss  5994  intirr  6077  elid  6156  funi  6538  f1ovi  6828  idssen  8944  symgcom2  31977  idsset  34504  bj-ideqgALT  35658  bj-ideqb  35659  bj-ideqg1ALT  35665  bj-opelidb1ALT  35666  bj-elid5  35669  brid  36796  iss2  36834  refrelid  37013  idsymrel  37052  disjALTVid  37246
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