Theorem reli 5736

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 5489	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5730	1 ⊢ Rel I

Syntax hints:   I cid 5488  Rel wrel 5594

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-in 3894  df-ss 3904  df-opab 5137  df-id 5489  df-xp 5595  df-rel 5596

This theorem is referenced by:  ideqg  5760  issetid  5763  iss  5943  intirr  6023  elid  6102  funi  6466  f1ovi  6755  idssen  8785  symgcom2  31353  idsset  34192  bj-ideqgALT  35329  bj-ideqb  35330  bj-ideqg1ALT  35336  bj-opelidb1ALT  35337  bj-elid5  35340  brid  36442  iss2  36479  refrelid  36639  idsymrel  36675  disjALTVid  36863