Theorem reli 5780

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 5526	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5774	1 ⊢ Rel I

Syntax hints:   I cid 5525  Rel wrel 5636

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3446  df-ss 3928  df-opab 5165  df-id 5526  df-xp 5637  df-rel 5638

This theorem is referenced by:  ideqg  5805  issetid  5808  iss  5995  intirr  6079  elid  6160  funi  6532  f1ovi  6821  idssen  8945  symgcom2  33014  idsset  35851  bj-ideqgALT  37119  bj-ideqb  37120  bj-ideqg1ALT  37126  bj-opelidb1ALT  37127  bj-elid5  37130  brid  38267  iss2  38299  refrelid  38486  idsymrel  38525  disjALTVid  38720