Theorem reli 5775

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 5519	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5769	1 ⊢ Rel I

Syntax hints:   I cid 5518  Rel wrel 5629

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3442  df-ss 3918  df-opab 5161  df-id 5519  df-xp 5630  df-rel 5631

This theorem is referenced by:  ideqg  5800  issetid  5803  iss  5994  intirr  6075  elid  6157  funi  6524  f1ovi  6814  idssen  8934  symgcom2  33166  idsset  36082  bj-ideqgALT  37363  bj-ideqb  37364  bj-ideqg1ALT  37370  bj-opelidb1ALT  37371  bj-elid5  37374  brid  38505  iss2  38537  dfsucmap3  38637  refrelid  38775  idsymrel  38818  disjALTVid  39014