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Theorem reli 4965
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 4463 . 2  |-  _I  =  { <. x ,  y
>.  |  x  =  y }
21relopabi 4963 1  |-  Rel  _I
Colors of variables: wff set class
Syntax hints:    _I cid 4457   Rel wrel 4846
This theorem is referenced by:  ideqg  4987  issetid  4990  iss  5152  intirr  5215  funi  5446  f1ovi  5677  idssen  7115  idsset  25648
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389  ax-sep 4294  ax-nul 4302  ax-pr 4367
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-ne 2573  df-ral 2675  df-rex 2676  df-rab 2679  df-v 2922  df-dif 3287  df-un 3289  df-in 3291  df-ss 3298  df-nul 3593  df-if 3704  df-sn 3784  df-pr 3785  df-op 3787  df-opab 4231  df-id 4462  df-xp 4847  df-rel 4848
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