Theorem reli 5725

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 5480	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5719	1 ⊢ Rel I

Syntax hints:   I cid 5479  Rel wrel 5585

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-in 3890  df-ss 3900  df-opab 5133  df-id 5480  df-xp 5586  df-rel 5587

This theorem is referenced by:  ideqg  5749  issetid  5752  iss  5932  intirr  6012  elid  6091  funi  6450  f1ovi  6738  idssen  8740  symgcom2  31255  idsset  34119  bj-ideqgALT  35256  bj-ideqb  35257  bj-ideqg1ALT  35263  bj-opelidb1ALT  35264  bj-elid5  35267  brid  36369  iss2  36406  refrelid  36566  idsymrel  36602  disjALTVid  36790