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Mirrors > Home > MPE Home > Th. List > catidcl | Structured version Visualization version Unicode version |
Description: Each object in a category has an associated identity arrow. (Contributed by Mario Carneiro, 2-Jan-2017.) |
Ref | Expression |
---|---|
catidcl.b | |
catidcl.h | |
catidcl.i | |
catidcl.c | |
catidcl.x |
Ref | Expression |
---|---|
catidcl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | catidcl.b | . . 3 | |
2 | catidcl.h | . . 3 | |
3 | eqid 2622 | . . 3 comp comp | |
4 | catidcl.c | . . 3 | |
5 | catidcl.i | . . 3 | |
6 | catidcl.x | . . 3 | |
7 | 1, 2, 3, 4, 5, 6 | cidval 16338 | . 2 comp comp |
8 | 1, 2, 3, 4, 6 | catideu 16336 | . . 3 comp comp |
9 | riotacl 6625 | . . 3 comp comp comp comp | |
10 | 8, 9 | syl 17 | . 2 comp comp |
11 | 7, 10 | eqeltrd 2701 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wral 2912 wreu 2914 cop 4183 cfv 5888 crio 6610 (class class class)co 6650 cbs 15857 chom 15952 compcco 15953 ccat 16325 ccid 16326 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-rep 4771 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rmo 2920 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-riota 6611 df-ov 6653 df-cat 16329 df-cid 16330 |
This theorem is referenced by: oppccatid 16379 monsect 16443 sectid 16446 cicref 16461 catsubcat 16499 fullsubc 16510 idfucl 16541 cofucl 16548 fthsect 16585 fucidcl 16625 initoid 16655 termoid 16656 idahom 16710 catcisolem 16756 xpccatid 16828 1stfcl 16837 2ndfcl 16838 prfcl 16843 evlfcl 16862 curf1cl 16868 curf2cl 16871 curfcl 16872 curfuncf 16878 uncfcurf 16879 diag12 16884 diag2 16885 curf2ndf 16887 hofcl 16899 yon12 16905 yon2 16906 yonedalem3a 16914 yonedalem3b 16919 yonedainv 16921 |
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