Theorem reli 5811

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 5554	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5805	1 ⊢ Rel I

This proof depends on syntax axioms:   I cid 5553  Rel wrel 5664

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 2147  ax-9 2155  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3455  df-ss 3919  df-opab 5172  df-id 5554  df-xp 5665  df-rel 5666

This theorem is used by:  ideqg  5835  issetid  5838  iss  6035  intirr  6116  elid  6197  funi  6569  f1ovi  6862  idssen  9007  symgcom2  33532  idsset  36475  bj-ideqgALT  37918  bj-ideqb  37919  bj-ideqg1ALT  37925  bj-opelidb1ALT  37926  bj-elid5  37929  brid  39068  iss2  39100  dfsucmap3  39219  refrelid  39358  idsymrel  39401  disjALTVid  39611