Theorem reli 5701

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 5463	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabi 5697	1 ⊢ Rel I

Syntax hints:   I cid 5462  Rel wrel 5563

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 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2796

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2966  df-rab 3150  df-v 3499  df-dif 3942  df-un 3944  df-in 3946  df-ss 3955  df-nul 4295  df-if 4471  df-sn 4571  df-pr 4573  df-op 4577  df-opab 5132  df-id 5463  df-xp 5564  df-rel 5565

This theorem is referenced by:  ideqg  5725  issetid  5728  iss  5906  intirr  5981  elid  6059  funi  6390  f1ovi  6656  idssen  8557  symgcom2  30732  idsset  33355  bj-ideqgALT  34454  bj-ideqb  34455  bj-ideqg1ALT  34461  bj-opelidb1ALT  34462  bj-elid5  34465  brid  35568  iss2  35605  refrelid  35765  idsymrel  35801  disjALTVid  35989