Theorem reli 3268

Description: The identity relation is a relation. Part of Exercise 4.12(p) of [Mendelson] p. 235.

Assertion

Ref	Expression
reli	|- Rel I

Proof of Theorem reli

Step	Hyp	Ref	Expression
1		relopab 3261	. 2 |- Rel {<.x, y>. | x = y}
2		df-id 2830	. . 3 |- I = {<.x, y>. | x = y}
3	2	releqi 3239	. 2 |- (Rel I <-> Rel {<.x, y>. | x = y})
4	1, 3	mpbir 190	1 |- Rel I

Syntax hints:   = wceq 954  {copab 2661  Icid 2826  Rel wrel 3170

This theorem is referenced by:  ideqg 3271  issetid 3275  iss 3389  intirr 3433  cnvi 3439  funi 3537  f1ovi 3709  idssen 4393

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-11 965  ax-12 966  ax-13 967  ax-14 968  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457  ax-sep 2698  ax-pow 2737  ax-pr 2774

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-eu 1380  df-mo 1381  df-clab 1462  df-cleq 1467  df-clel 1470  df-ne 1584  df-v 1808  df-dif 2045  df-un 2046  df-in 2047  df-ss 2049  df-nul 2277  df-pw 2398  df-sn 2408  df-pr 2409  df-op 2412  df-opab 2662  df-id 2830  df-xp 3179  df-rel 3180

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