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Mathbox for Peter Mazsa |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > cosscnvid | Structured version Visualization version GIF version |
Description: Cosets by the converse identity relation are the identity relation. (Contributed by Peter Mazsa, 27-Sep-2021.) |
Ref | Expression |
---|---|
cosscnvid | ⊢ ≀ ◡ I = I |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvi 6146 | . . 3 ⊢ ◡ I = I | |
2 | 1 | cosseqi 37899 | . 2 ⊢ ≀ ◡ I = ≀ I |
3 | cossid 37952 | . 2 ⊢ ≀ I = I | |
4 | 2, 3 | eqtri 2756 | 1 ⊢ ≀ ◡ I = I |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1534 I cid 5575 ◡ccnv 5677 ≀ ccoss 37648 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2699 ax-sep 5299 ax-nul 5306 ax-pr 5429 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2706 df-cleq 2720 df-clel 2806 df-ral 3059 df-rex 3068 df-rab 3430 df-v 3473 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4324 df-if 4530 df-sn 4630 df-pr 4632 df-op 4636 df-br 5149 df-opab 5211 df-id 5576 df-xp 5684 df-rel 5685 df-cnv 5686 df-coss 37883 |
This theorem is referenced by: disjALTVid 38227 |
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