Theorem reli 5815

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 5558	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5809	1 ⊢ Rel I

This proof depends on syntax axioms:   I cid 5557  Rel wrel 5668

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-ss 3923  df-opab 5176  df-id 5558  df-xp 5669  df-rel 5670

This theorem is used by:  ideqg  5839  issetid  5842  iss  6039  intirr  6120  elid  6200  funi  6572  f1ovi  6865  idssen  9000  symgcom2  33470  idsset  36419  bj-ideqgALT  37861  bj-ideqb  37862  bj-ideqg1ALT  37868  bj-opelidb1ALT  37869  bj-elid5  37872  brid  39021  iss2  39053  dfsucmap3  39172  refrelid  39311  idsymrel  39354  disjALTVid  39564