Colors of
variables: wff set class |
Syntax hints: wi 4
wa 104
wceq 1353
wcel 2148
wral 2455
cfv 5218
(class class class)co 5877 cbs 12464 cplusg 12538 cmulr 12539 c0g 12710 cmnd 12822 cgrp 12882 CMndccmn 13093
mulGrpcmgp 13135 SRingcsrg 13151
crg 13184 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709
ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-coll 4120 ax-sep 4123 ax-pow 4176 ax-pr 4211 ax-un 4435 ax-setind 4538 ax-cnex 7904 ax-resscn 7905 ax-1cn 7906 ax-1re 7907 ax-icn 7908 ax-addcl 7909 ax-addrcl 7910 ax-mulcl 7911 ax-addcom 7913 ax-addass 7915 ax-i2m1 7918 ax-0lt1 7919 ax-0id 7921 ax-rnegex 7922 ax-pre-ltirr 7925 ax-pre-ltadd 7929 |
This theorem depends on definitions:
df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-rex 2461 df-reu 2462 df-rmo 2463 df-rab 2464 df-v 2741 df-sbc 2965 df-csb 3060 df-dif 3133 df-un 3135 df-in 3137 df-ss 3144 df-nul 3425 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-int 3847 df-iun 3890 df-br 4006 df-opab 4067 df-mpt 4068 df-id 4295 df-xp 4634 df-rel 4635 df-cnv 4636 df-co 4637 df-dm 4638 df-rn 4639 df-res 4640 df-ima 4641 df-iota 5180 df-fun 5220 df-fn 5221 df-f 5222 df-f1 5223 df-fo 5224 df-f1o 5225 df-fv 5226 df-riota 5833 df-ov 5880 df-oprab 5881 df-mpo 5882 df-pnf 7996 df-mnf 7997 df-ltxr 7999 df-inn 8922 df-2 8980 df-3 8981
df-ndx 12467 df-slot 12468 df-base 12470 df-sets 12471 df-plusg 12551 df-mulr 12552 df-0g 12712 df-mgm 12780 df-sgrp 12813 df-mnd 12823 df-grp 12885 df-minusg 12886 df-cmn 13095 df-abl 13096 df-mgp 13136 df-ur 13148 df-srg 13152 df-ring 13186 |
This theorem is referenced by: dvdsrcl2
13273 dvdsrid
13274 dvdsrtr
13275 dvdsrmul1
13276 dvdsrneg
13277 dvdsr01
13278 dvdsr02
13279 1unit
13281 opprunitd
13284 crngunit
13285 unitmulcl
13287 unitmulclb
13288 unitgrp
13290 unitabl
13291 unitgrpid
13292 unitsubm
13293 unitinvcl
13297 unitinvinv
13298 ringinvcl
13299 unitlinv
13300 unitrinv
13301 unitnegcl
13304 dvrvald
13308 unitdvcl
13310 dvrid
13311 dvrcan1
13314 dvrcan3
13315 dvreq1
13316 dvrdir
13317 rdivmuldivd
13318 unitpropdg
13322 invrpropdg
13323 subrgdvds
13361 subrguss
13362 subrginv
13363 subrgunit
13365 subrgugrp
13366 subrgintm
13369 dvdsrzring
13532 |