Theorem cosscnvid 36599

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 6045	. . 3 ⊢ ◡ I = I
2	1	cosseqi 36550	. 2 ⊢ ≀ ◡ I = ≀ I
3		cossid 36598	. 2 ⊢ ≀ I = I
4	2, 3	eqtri 2766	1 ⊢ ≀ ◡ I = I

Syntax hints:   = wceq 1539   I cid 5488  ^◡ccnv 5588   ≀ ccoss 36333

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709  ax-sep 5223  ax-nul 5230  ax-pr 5352

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-ral 3069  df-rex 3070  df-rab 3073  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-nul 4257  df-if 4460  df-sn 4562  df-pr 4564  df-op 4568  df-br 5075  df-opab 5137  df-id 5489  df-xp 5595  df-rel 5596  df-cnv 5597  df-coss 36537

This theorem is referenced by:  disjALTVid  36863