Theorem reli 5799

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 5542	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5793	1 ⊢ Rel I

Syntax hints:   I cid 5541  Rel wrel 5652

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-ext 2734

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1563  df-ex 1800  df-sb 2091  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3456  df-ss 3921  df-opab 5163  df-id 5542  df-xp 5653  df-rel 5654

This theorem is referenced by:  ideqg  5823  issetid  5826  iss  6024  intirr  6105  elid  6186  funi  6553  f1ovi  6847  idssen  8978  symgcom2  33264  idsset  36238  bj-ideqgALT  37650  bj-ideqb  37651  bj-ideqg1ALT  37657  bj-opelidb1ALT  37658  bj-elid5  37661  brid  38811  iss2  38843  dfsucmap3  38962  refrelid  39101  idsymrel  39144  disjALTVid  39354