Theorem reli 5693

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.

Step	Hyp	Ref	Expression
1		df-id 5455	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabi 5689	1 ⊢ Rel I

Syntax hints:   I cid 5454  Rel wrel 5555

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2156  ax-12 2172  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1536  df-ex 1777  df-nf 1781  df-sb 2066  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-rab 3147  df-v 3497  df-dif 3939  df-un 3941  df-in 3943  df-ss 3952  df-nul 4292  df-if 4468  df-sn 4562  df-pr 4564  df-op 4568  df-opab 5122  df-id 5455  df-xp 5556  df-rel 5557

This theorem is referenced by:  ideqg  5717  issetid  5720  iss  5898  intirr  5973  elid  6051  funi  6382  f1ovi  6648  idssen  8548  symgcom2  30723  idsset  33346  bj-ideqgALT  34444  bj-ideqb  34445  bj-ideqg1ALT  34451  bj-opelidb1ALT  34452  bj-elid5  34455  brid  35558  iss2  35595  refrelid  35755  idsymrel  35791  disjALTVid  35979