Theorem reli 5814

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 5557	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5808	1 ⊢ Rel I

Syntax hints:   I cid 5556  Rel wrel 5667

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-v 3465  df-ss 3930  df-opab 5178  df-id 5557  df-xp 5668  df-rel 5669

This theorem is referenced by:  ideqg  5838  issetid  5841  iss  6038  intirr  6119  elid  6199  funi  6569  f1ovi  6862  idssen  8994  symgcom2  33345  idsset  36279  bj-ideqgALT  37690  bj-ideqb  37691  bj-ideqg1ALT  37697  bj-opelidb1ALT  37698  bj-elid5  37701  brid  38851  iss2  38883  dfsucmap3  39002  refrelid  39141  idsymrel  39184  disjALTVid  39394