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Theorem reli 4812
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
Dummy variables  x  y are mutually distinct and distinct from all other variables.

Proof of Theorem reli
StepHypRef Expression
1 dfid3 4309 . 2  |-  _I  =  { <. x ,  y
>.  |  x  =  y }
21relopabi 4810 1  |-  Rel  _I
Colors of variables: wff set class
Syntax hints:    = wceq 1624    _I cid 4303   Rel wrel 4693
This theorem is referenced by:  ideqg  4834  issetid  4837  iss  4997  intirr  5060  funi  5250  f1ovi  5477  idssen  6901  idsset  23838
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-14 1689  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1867  ax-ext 2265  ax-sep 4142  ax-nul 4150  ax-pr 4213
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 938  df-tru 1312  df-ex 1530  df-nf 1533  df-sb 1632  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-ne 2449  df-ral 2549  df-rex 2550  df-rab 2553  df-v 2791  df-dif 3156  df-un 3158  df-in 3160  df-ss 3167  df-nul 3457  df-if 3567  df-sn 3647  df-pr 3648  df-op 3650  df-opab 4079  df-id 4308  df-xp 4694  df-rel 4695
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