Theorem reli 5769

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 5513	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5763	1 ⊢ Rel I

Syntax hints:   I cid 5512  Rel wrel 5623

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-v 3433  df-ss 3900  df-opab 5135  df-id 5513  df-xp 5624  df-rel 5625

This theorem is referenced by:  ideqg  5793  issetid  5796  iss  5987  intirr  6068  elid  6150  funi  6517  f1ovi  6807  idssen  8934  symgcom2  33165  idsset  36116  bj-ideqgALT  37518  bj-ideqb  37519  bj-ideqg1ALT  37525  bj-opelidb1ALT  37526  bj-elid5  37529  brid  38679  iss2  38711  dfsucmap3  38830  refrelid  38969  idsymrel  39012  disjALTVid  39222