Theorem cosscnvid 38517

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

Step	Hyp	Ref	Expression
1		cnvi 6088	. . 3 ⊢ ◡ I = I
2	1	cosseqi 38463	. 2 ⊢ ≀ ◡ I = ≀ I
3		cossid 38516	. 2 ⊢ ≀ I = I
4	2, 3	eqtri 2754	1 ⊢ ≀ ◡ I = I

Syntax hints:   = wceq 1541   I cid 5510  ^◡ccnv 5615   ≀ ccoss 38214

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703  ax-sep 5234  ax-nul 5244  ax-pr 5370

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-ral 3048  df-rex 3057  df-rab 3396  df-v 3438  df-dif 3905  df-un 3907  df-ss 3919  df-nul 4284  df-if 4476  df-sn 4577  df-pr 4579  df-op 4583  df-br 5092  df-opab 5154  df-id 5511  df-xp 5622  df-rel 5623  df-cnv 5624  df-coss 38447

This theorem is referenced by:  disjALTVid  38792