Theorem reli 5789

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 5533	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5783	1 ⊢ Rel I

Syntax hints:   I cid 5532  Rel wrel 5643

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 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3449  df-ss 3931  df-opab 5170  df-id 5533  df-xp 5644  df-rel 5645

This theorem is referenced by:  ideqg  5815  issetid  5818  iss  6006  intirr  6091  elid  6172  funi  6548  f1ovi  6839  idssen  8968  symgcom2  33041  idsset  35878  bj-ideqgALT  37146  bj-ideqb  37147  bj-ideqg1ALT  37153  bj-opelidb1ALT  37154  bj-elid5  37157  brid  38294  iss2  38326  refrelid  38513  idsymrel  38552  disjALTVid  38747