Theorem reli 5773

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 5517	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5767	1 ⊢ Rel I

Syntax hints:   I cid 5516  Rel wrel 5627

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 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2713  df-cleq 2726  df-clel 2809  df-v 3440  df-ss 3916  df-opab 5159  df-id 5517  df-xp 5628  df-rel 5629

This theorem is referenced by:  ideqg  5798  issetid  5801  iss  5992  intirr  6073  elid  6155  funi  6522  f1ovi  6812  idssen  8932  symgcom2  33115  idsset  36031  bj-ideqgALT  37302  bj-ideqb  37303  bj-ideqg1ALT  37309  bj-opelidb1ALT  37310  bj-elid5  37313  brid  38444  iss2  38476  dfsucmap3  38576  refrelid  38714  idsymrel  38757  disjALTVid  38953