Theorem reli 5805

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 5548	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5799	1 ⊢ Rel I

Syntax hints:   I cid 5547  Rel wrel 5659

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 2007  ax-8 2110  ax-9 2118  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-v 3461  df-ss 3943  df-opab 5182  df-id 5548  df-xp 5660  df-rel 5661

This theorem is referenced by:  ideqg  5831  issetid  5834  iss  6022  intirr  6107  elid  6188  funi  6568  f1ovi  6857  idssen  9011  symgcom2  33095  idsset  35908  bj-ideqgALT  37176  bj-ideqb  37177  bj-ideqg1ALT  37183  bj-opelidb1ALT  37184  bj-elid5  37187  brid  38324  iss2  38362  refrelid  38540  idsymrel  38579  disjALTVid  38773