Theorem reli 5824

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 5573	. 2 ⊢ I = {⟨𝑥, 𝑦⟩ ∣ 𝑥 = 𝑦}
2	1	relopabiv 5818	1 ⊢ Rel I

Syntax hints:   I cid 5572  Rel wrel 5680

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-in 3954  df-ss 3964  df-opab 5210  df-id 5573  df-xp 5681  df-rel 5682

This theorem is referenced by:  ideqg  5849  issetid  5852  iss  6033  intirr  6116  elid  6195  funi  6577  f1ovi  6869  idssen  8989  symgcom2  32232  idsset  34850  bj-ideqgALT  36027  bj-ideqb  36028  bj-ideqg1ALT  36034  bj-opelidb1ALT  36035  bj-elid5  36038  brid  37163  iss2  37201  refrelid  37380  idsymrel  37419  disjALTVid  37613