Theorem reli 5813

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 5556	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5807	1 ⊢ Rel I

Syntax hints:   I cid 5555  Rel wrel 5666

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-ss 3922  df-opab 5174  df-id 5556  df-xp 5667  df-rel 5668

This theorem is referenced by:  ideqg  5837  issetid  5840  iss  6037  intirr  6118  elid  6198  funi  6568  f1ovi  6861  idssen  8990  symgcom2  33404  idsset  36380  bj-ideqgALT  37822  bj-ideqb  37823  bj-ideqg1ALT  37829  bj-opelidb1ALT  37830  bj-elid5  37833  brid  38981  iss2  39013  dfsucmap3  39132  refrelid  39271  idsymrel  39314  disjALTVid  39524