Theorem reli 5850

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 5593	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5844	1 ⊢ Rel I

Syntax hints:   I cid 5592  Rel wrel 5705

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-ss 3993  df-opab 5229  df-id 5593  df-xp 5706  df-rel 5707

This theorem is referenced by:  ideqg  5876  issetid  5879  iss  6064  intirr  6150  elid  6230  funi  6610  f1ovi  6901  idssen  9057  symgcom2  33077  idsset  35854  bj-ideqgALT  37124  bj-ideqb  37125  bj-ideqg1ALT  37131  bj-opelidb1ALT  37132  bj-elid5  37135  brid  38262  iss2  38300  refrelid  38478  idsymrel  38517  disjALTVid  38711