Theorem reli 5783

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 5527	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5777	1 ⊢ Rel I

Syntax hints:   I cid 5526  Rel wrel 5637

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 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3444  df-ss 3920  df-opab 5163  df-id 5527  df-xp 5638  df-rel 5639

This theorem is referenced by:  ideqg  5808  issetid  5811  iss  6002  intirr  6083  elid  6165  funi  6532  f1ovi  6822  idssen  8946  symgcom2  33178  idsset  36104  bj-ideqgALT  37413  bj-ideqb  37414  bj-ideqg1ALT  37420  bj-opelidb1ALT  37421  bj-elid5  37424  brid  38563  iss2  38595  dfsucmap3  38714  refrelid  38853  idsymrel  38896  disjALTVid  39106