Theorem reli 5804

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 5546	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5798	1 ⊢ Rel I

This proof depends on syntax axioms:   I cid 5545  Rel wrel 5656

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 2733

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3453  df-ss 3916  df-opab 5168  df-id 5546  df-xp 5657  df-rel 5658

This theorem is used by:  ideqg  5829  issetid  5832  iss  6027  intirr  6112  elid  6193  funi  6572  f1ovi  6865  idssen  9024  symgcom2  33645  idsset  36652  bj-ideqgALT  38079  bj-ideqb  38080  bj-ideqg1ALT  38086  bj-opelidb1ALT  38087  bj-elid5  38090  brid  39244  iss2  39276  dfsucmap3  39395  refrelid  39534  idsymrel  39577  disjALTVid  39787