Theorem reli 5662

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 5425	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabi 5658	1 ⊢ Rel I

Syntax hints:   I cid 5424  Rel wrel 5524

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-11 2158  ax-12 2175  ax-ext 2770

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-un 3886  df-in 3888  df-ss 3898  df-sn 4526  df-pr 4528  df-op 4532  df-opab 5093  df-id 5425  df-xp 5525  df-rel 5526

This theorem is referenced by:  ideqg  5686  issetid  5689  iss  5870  intirr  5945  elid  6023  funi  6356  f1ovi  6628  idssen  8537  symgcom2  30778  idsset  33464  bj-ideqgALT  34573  bj-ideqb  34574  bj-ideqg1ALT  34580  bj-opelidb1ALT  34581  bj-elid5  34584  brid  35724  iss2  35761  refrelid  35921  idsymrel  35957  disjALTVid  36145