Theorem reli 5807

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 5550	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5801	1 ⊢ Rel I

This proof depends on syntax axioms:   I cid 5549  Rel wrel 5660

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 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3916  df-opab 5168  df-id 5550  df-xp 5661  df-rel 5662

This theorem is used by:  ideqg  5831  issetid  5834  iss  6031  intirr  6112  elid  6193  funi  6566  f1ovi  6859  idssen  9006  symgcom2  33527  idsset  36470  bj-ideqgALT  37913  bj-ideqb  37914  bj-ideqg1ALT  37920  bj-opelidb1ALT  37921  bj-elid5  37924  brid  39063  iss2  39095  dfsucmap3  39214  refrelid  39353  idsymrel  39396  disjALTVid  39606