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Theorem reli 4895
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 4392 . 2  |-  _I  =  { <. x ,  y
>.  |  x  =  y }
21relopabi 4893 1  |-  Rel  _I
Colors of variables: wff set class
Syntax hints:    = wceq 1642    _I cid 4386   Rel wrel 4776
This theorem is referenced by:  ideqg  4917  issetid  4920  iss  5080  intirr  5143  funi  5366  f1ovi  5595  idssen  6994  idsset  24988
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-sep 4222  ax-nul 4230  ax-pr 4295
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-ral 2624  df-rex 2625  df-rab 2628  df-v 2866  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-opab 4159  df-id 4391  df-xp 4777  df-rel 4778
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