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Theorem cosscnvid 35767
Description: Cosets by the converse identity relation are the identity relation. (Contributed by Peter Mazsa, 27-Sep-2021.)
Assertion
Ref Expression
cosscnvid I = I

Proof of Theorem cosscnvid
StepHypRef Expression
1 cnvi 5973 . . 3 I = I
21cosseqi 35718 . 2 I = ≀ I
3 cossid 35766 . 2 ≀ I = I
42, 3eqtri 2844 1 I = I
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538   I cid 5432  ccnv 5527  ccoss 35499
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 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2178  ax-ext 2793  ax-sep 5176  ax-nul 5183  ax-pr 5303
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2623  df-eu 2654  df-clab 2800  df-cleq 2814  df-clel 2892  df-nfc 2960  df-ral 3131  df-rex 3132  df-rab 3135  df-v 3473  df-dif 3913  df-un 3915  df-in 3917  df-ss 3927  df-nul 4267  df-if 4441  df-sn 4541  df-pr 4543  df-op 4547  df-br 5040  df-opab 5102  df-id 5433  df-xp 5534  df-rel 5535  df-cnv 5536  df-coss 35705
This theorem is referenced by:  disjALTVid  36031
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