Theorem reli 5827

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 5575	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5821	1 ⊢ Rel I

Syntax hints:   I cid 5574  Rel wrel 5682

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3956  df-ss 3966  df-opab 5212  df-id 5575  df-xp 5683  df-rel 5684

This theorem is referenced by:  ideqg  5852  issetid  5855  iss  6036  intirr  6120  elid  6199  funi  6581  f1ovi  6873  idssen  8993  symgcom2  32245  idsset  34862  bj-ideqgALT  36039  bj-ideqb  36040  bj-ideqg1ALT  36046  bj-opelidb1ALT  36047  bj-elid5  36050  brid  37175  iss2  37213  refrelid  37392  idsymrel  37431  disjALTVid  37625