Theorem reli 5792

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 5536	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5786	1 ⊢ Rel I

Syntax hints:   I cid 5535  Rel wrel 5646

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 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-ss 3934  df-opab 5173  df-id 5536  df-xp 5647  df-rel 5648

This theorem is referenced by:  ideqg  5818  issetid  5821  iss  6009  intirr  6094  elid  6175  funi  6551  f1ovi  6842  idssen  8971  symgcom2  33048  idsset  35885  bj-ideqgALT  37153  bj-ideqb  37154  bj-ideqg1ALT  37160  bj-opelidb1ALT  37161  bj-elid5  37164  brid  38301  iss2  38333  refrelid  38520  idsymrel  38559  disjALTVid  38754