Theorem cosscnvid 38441

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 6179	. . 3 ⊢ ◡ I = I
2	1	cosseqi 38387	. 2 ⊢ ≀ ◡ I = ≀ I
3		cossid 38440	. 2 ⊢ ≀ I = I
4	2, 3	eqtri 2762	1 ⊢ ≀ ◡ I = I

Syntax hints:   = wceq 1537   I cid 5603  ^◡ccnv 5705   ≀ ccoss 38139

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2105  ax-9 2113  ax-ext 2705  ax-sep 5327  ax-nul 5334  ax-pr 5457

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2712  df-cleq 2726  df-clel 2813  df-ral 3064  df-rex 3073  df-rab 3440  df-v 3486  df-dif 3979  df-un 3981  df-ss 3993  df-nul 4354  df-if 4555  df-sn 4655  df-pr 4657  df-op 4661  df-br 5177  df-opab 5239  df-id 5604  df-xp 5712  df-rel 5713  df-cnv 5714  df-coss 38371

This theorem is referenced by:  disjALTVid  38715