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Theorem eqvrelid 38301
Description: The identity relation is an equivalence relation. (Contributed by Peter Mazsa, 15-Apr-2019.) (Revised by Peter Mazsa, 31-Dec-2021.)
Assertion
Ref Expression
eqvrelid EqvRel I

Proof of Theorem eqvrelid
StepHypRef Expression
1 disjALTVid 38267 . . 3 Disj I
21disjimi 38294 . 2 EqvRel ≀ I
3 cossid 37992 . . 3 ≀ I = I
43eqvreleqi 38115 . 2 ( EqvRel ≀ I ↔ EqvRel I )
52, 4mpbi 229 1 EqvRel I
Colors of variables: wff setvar class
Syntax hints:   I cid 5579  ccoss 37689   EqvRel weqvrel 37706
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2166  ax-ext 2699  ax-sep 5303  ax-nul 5310  ax-pr 5433
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2529  df-eu 2558  df-clab 2706  df-cleq 2720  df-clel 2806  df-nfc 2881  df-ral 3059  df-rex 3068  df-rab 3431  df-v 3475  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4327  df-if 4533  df-sn 4633  df-pr 4635  df-op 4639  df-br 5153  df-opab 5215  df-id 5580  df-xp 5688  df-rel 5689  df-cnv 5690  df-co 5691  df-dm 5692  df-rn 5693  df-res 5694  df-coss 37923  df-refrel 38024  df-cnvrefrel 38039  df-symrel 38056  df-trrel 38086  df-eqvrel 38097  df-disjALTV 38217
This theorem is referenced by: (None)
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