| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∈ wcel 2106
CMndccmn 19689 Abelcabl 19690
Ringcrg 20127 |
| 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 1913
ax-6 1971 ax-7 2011 ax-8 2108
ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2703 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7727 ax-cnex 11168 ax-resscn 11169 ax-1cn 11170 ax-icn 11171 ax-addcl 11172 ax-addrcl 11173 ax-mulcl 11174 ax-mulrcl 11175 ax-mulcom 11176 ax-addass 11177 ax-mulass 11178 ax-distr 11179 ax-i2m1 11180 ax-1ne0 11181 ax-1rid 11182 ax-rnegex 11183 ax-rrecex 11184 ax-cnre 11185 ax-pre-lttri 11186 ax-pre-lttrn 11187 ax-pre-ltadd 11188 ax-pre-mulgt0 11189 |
| This theorem depends on definitions:
df-bi 206 df-an 397
df-or 846 df-3or 1088 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2534 df-eu 2563 df-clab 2710 df-cleq 2724 df-clel 2810 df-nfc 2885 df-ne 2941 df-nel 3047 df-ral 3062 df-rex 3071 df-rmo 3376 df-reu 3377 df-rab 3433 df-v 3476 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-pss 3967 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-iun 4999 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5574 df-eprel 5580 df-po 5588 df-so 5589 df-fr 5631 df-we 5633 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-pred 6300 df-ord 6367 df-on 6368 df-lim 6369 df-suc 6370 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-riota 7367 df-ov 7414 df-oprab 7415 df-mpo 7416 df-om 7858 df-2nd 7978 df-frecs 8268 df-wrecs 8299 df-recs 8373 df-rdg 8412 df-er 8705 df-en 8942 df-dom 8943 df-sdom 8944 df-pnf 11254 df-mnf 11255 df-xr 11256 df-ltxr 11257 df-le 11258 df-sub 11450 df-neg 11451 df-nn 12217 df-2 12279
df-sets 17101 df-slot 17119 df-ndx 17131 df-base 17149 df-plusg 17214 df-0g 17391 df-mgm 18565 df-sgrp 18644 df-mnd 18660 df-grp 18858 df-minusg 18859 df-cmn 19691 df-abl 19692 df-mgp 20029 df-ur 20076 df-ring 20129 |
| This theorem is referenced by: ringsrg
20185 gsummulc1OLD
20202 gsummulc2OLD
20203 gsumfsum
21212 nn0srg
21215 rge0srg
21216 regsumsupp
21394 ip2di
21413 psrlidm
21742 psrridm
21743 psrdi
21745 psrdir
21746 psrcom
21748 mplmonmul
21810 mplcoe1
21811 evlslem2
21861 evlslem1
21864 evlsgsumadd
21873 mhpmulcl
21911 psropprmul
21980 coe1mul2
22011 coe1fzgsumdlem
22045 gsumsmonply1
22047 gsummoncoe1
22048 lply1binom
22050 evls1gsumadd
22063 evl1gsumdlem
22095 mamucl
22121 mamudi
22123 mamudir
22124 mat1dimmul
22198 dmatmul
22219 mavmulcl
22269 mdetleib2
22310 mdetf
22317 mdetrlin
22324 mdetralt
22330 m2detleib
22353 madugsum
22365 smadiadetlem3lem2
22389 smadiadet
22392 mat2pmatmul
22453 m2pmfzgsumcl
22470 decpmatmul
22494 pmatcollpw1
22498 pmatcollpwfi
22504 pmatcollpw3fi1lem1
22508 pm2mpcl
22519 mply1topmatcl
22527 mp2pm2mplem2
22529 mp2pm2mplem4
22531 mp2pm2mp
22533 pm2mpghm
22538 pm2mpmhmlem2
22541 pm2mp
22547 chfacfscmulgsum
22582 chfacfpmmulgsum
22586 cpmadugsumlemF
22598 cpmadugsumfi
22599 cayhamlem4
22610 tdeglem1
25797 tdeglem1OLD
25798 tdeglem3
25799 tdeglem3OLD
25800 tdeglem4
25801 tdeglem4OLD
25802 plypf1
25950 taylfvallem
26094 taylf
26097 tayl0
26098 taylpfval
26101 jensenlem1
26715 jensenlem2
26716 jensen
26717 amgm
26719 freshmansdream
32639 ofldchr
32690 elrspunidl
32808 ply1degltdimlem
32983 fedgmullem1
32990 fedgmullem2
32991 mdetpmtr1
33089 zarcmplem
33147 matunitlindflem1
36787 lfladdcl
38244 mhphflem
41470 ply1mulgsum
47159 amgmwlem
47937 |
