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 5553	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabi 5809	1 ⊢ Rel I

This proof depends on syntax axioms:   I cid 5552  Rel wrel 5663

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-v 3456  df-ss 3901  df-dif 4050  df-un 4154  df-nul 4282  df-if 4486  df-sn 4589  df-pr 4591  df-op 4841  df-opab 5174  df-id 5553  df-xp 5664  df-rel 5665

This theorem is used by:  ideqg  5839  issetid  5842  iss  6045  intirr  6130  elid  6212  funi  6600  f1ovi  6896  idssen  9062  symgcom2  33744  idsset  36867  cossidmid  38226  bj-ideqgALT  38347  bj-ideqb  38348  bj-ideqg1ALT  38354  bj-opelidb1ALT  38355  bj-elid5  38358  brid  39510  iss2  39542  dfsucmap3  39661  refrelid  39800  idsymrel  39843  disjALTVid  40053