Theorem reli 5769

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 5514	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5763	1 ⊢ Rel I

Syntax hints:   I cid 5513  Rel wrel 5624

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 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3438  df-ss 3920  df-opab 5155  df-id 5514  df-xp 5625  df-rel 5626

This theorem is referenced by:  ideqg  5794  issetid  5797  iss  5986  intirr  6067  elid  6148  funi  6514  f1ovi  6803  idssen  8922  symgcom2  33026  idsset  35868  bj-ideqgALT  37136  bj-ideqb  37137  bj-ideqg1ALT  37143  bj-opelidb1ALT  37144  bj-elid5  37147  brid  38284  iss2  38316  refrelid  38503  idsymrel  38542  disjALTVid  38737