Theorem reli 5836

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 5578	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5830	1 ⊢ Rel I

Syntax hints:   I cid 5577  Rel wrel 5690

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-ss 3968  df-opab 5206  df-id 5578  df-xp 5691  df-rel 5692

This theorem is referenced by:  ideqg  5862  issetid  5865  iss  6053  intirr  6138  elid  6219  funi  6598  f1ovi  6887  idssen  9037  symgcom2  33104  idsset  35891  bj-ideqgALT  37159  bj-ideqb  37160  bj-ideqg1ALT  37166  bj-opelidb1ALT  37167  bj-elid5  37170  brid  38307  iss2  38345  refrelid  38523  idsymrel  38562  disjALTVid  38756