Theorem reli 5828

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 5576	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5822	1 ⊢ Rel I

Syntax hints:   I cid 5575  Rel wrel 5683

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-v 3463  df-ss 3961  df-opab 5212  df-id 5576  df-xp 5684  df-rel 5685

This theorem is referenced by:  ideqg  5854  issetid  5857  iss  6040  intirr  6125  elid  6205  funi  6586  f1ovi  6877  idssen  9018  symgcom2  32897  idsset  35614  bj-ideqgALT  36765  bj-ideqb  36766  bj-ideqg1ALT  36772  bj-opelidb1ALT  36773  bj-elid5  36776  brid  37905  iss2  37943  refrelid  38121  idsymrel  38160  disjALTVid  38354