Theorem reli 5839

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 5583	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5833	1 ⊢ Rel I

Syntax hints:   I cid 5582  Rel wrel 5694

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 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-ss 3980  df-opab 5211  df-id 5583  df-xp 5695  df-rel 5696

This theorem is referenced by:  ideqg  5865  issetid  5868  iss  6055  intirr  6141  elid  6221  funi  6600  f1ovi  6888  idssen  9036  symgcom2  33087  idsset  35872  bj-ideqgALT  37141  bj-ideqb  37142  bj-ideqg1ALT  37148  bj-opelidb1ALT  37149  bj-elid5  37152  brid  38288  iss2  38326  refrelid  38504  idsymrel  38543  disjALTVid  38737