Theorem cosscnvid 38740

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 6099	. . 3 ⊢ ◡ I = I
2	1	cosseqi 38686	. 2 ⊢ ≀ ◡ I = ≀ I
3		cossid 38739	. 2 ⊢ ≀ I = I
4	2, 3	eqtri 2759	1 ⊢ ≀ ◡ I = I

Syntax hints:   = wceq 1541   I cid 5518  ^◡ccnv 5623   ≀ ccoss 38379

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 2115  ax-9 2123  ax-ext 2708  ax-sep 5241  ax-nul 5251  ax-pr 5377

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 2715  df-cleq 2728  df-clel 2811  df-ral 3052  df-rex 3061  df-rab 3400  df-v 3442  df-dif 3904  df-un 3906  df-ss 3918  df-nul 4286  df-if 4480  df-sn 4581  df-pr 4583  df-op 4587  df-br 5099  df-opab 5161  df-id 5519  df-xp 5630  df-rel 5631  df-cnv 5632  df-coss 38670

This theorem is referenced by:  disjALTVid  39010