Theorem reli 5808

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 5549	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5802	1 ⊢ Rel I

This proof depends on syntax axioms:   I cid 5548  Rel wrel 5659

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148  ax-9 2156  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2101  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3455  df-ss 3900  df-opab 5170  df-id 5549  df-xp 5660  df-rel 5661

This theorem is used by:  ideqg  5833  issetid  5836  iss  6032  intirr  6117  elid  6199  funi  6580  f1ovi  6873  idssen  9035  symgcom2  33698  idsset  36779  bj-ideqgALT  38219  bj-ideqb  38220  bj-ideqg1ALT  38226  bj-opelidb1ALT  38227  bj-elid5  38230  brid  39384  iss2  39416  dfsucmap3  39535  refrelid  39674  idsymrel  39717  disjALTVid  39927