Theorem cosscnvid 38816

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 6107	. . 3 ⊢ ◡ I = I
2	1	cosseqi 38762	. 2 ⊢ ≀ ◡ I = ≀ I
3		cossid 38815	. 2 ⊢ ≀ I = I
4	2, 3	eqtri 2760	1 ⊢ ≀ ◡ I = I

Syntax hints:   = wceq 1542   I cid 5526  ^◡ccnv 5631   ≀ ccoss 38428

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 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-sep 5243  ax-pr 5379

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-ral 3053  df-rex 3063  df-rab 3402  df-v 3444  df-dif 3906  df-un 3908  df-in 3910  df-ss 3920  df-nul 4288  df-if 4482  df-sn 4583  df-pr 4585  df-op 4589  df-br 5101  df-opab 5163  df-id 5527  df-xp 5638  df-rel 5639  df-cnv 5640  df-coss 38746

This theorem is referenced by:  disjALTVid  39100