Theorem reli 5782

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 5526	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5776	1 ⊢ Rel I

Syntax hints:   I cid 5525  Rel wrel 5636

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3431  df-ss 3906  df-opab 5148  df-id 5526  df-xp 5637  df-rel 5638

This theorem is referenced by:  ideqg  5806  issetid  5809  iss  6000  intirr  6081  elid  6163  funi  6530  f1ovi  6820  idssen  8944  symgcom2  33145  idsset  36070  bj-ideqgALT  37472  bj-ideqb  37473  bj-ideqg1ALT  37479  bj-opelidb1ALT  37480  bj-elid5  37483  brid  38633  iss2  38665  dfsucmap3  38784  refrelid  38923  idsymrel  38966  disjALTVid  39176