Theorem reli 5735

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 5490	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5729	1 ⊢ Rel I

Syntax hints:   I cid 5489  Rel wrel 5595

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2015  ax-8 2112  ax-9 2120  ax-ext 2711

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1545  df-ex 1787  df-sb 2072  df-clab 2718  df-cleq 2732  df-clel 2818  df-v 3433  df-in 3899  df-ss 3909  df-opab 5142  df-id 5490  df-xp 5596  df-rel 5597

This theorem is referenced by:  ideqg  5759  issetid  5762  iss  5942  intirr  6022  elid  6101  funi  6464  f1ovi  6752  idssen  8768  symgcom2  31349  idsset  34188  bj-ideqgALT  35325  bj-ideqb  35326  bj-ideqg1ALT  35332  bj-opelidb1ALT  35333  bj-elid5  35336  brid  36438  iss2  36475  refrelid  36635  idsymrel  36671  disjALTVid  36859