| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∈ wcel 2107
CMndccmn 19648 Abelcabl 19649
Ringcrg 20056 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914
ax-6 1972 ax-7 2012 ax-8 2109
ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-sep 5300 ax-nul 5307 ax-pow 5364 ax-pr 5428 ax-un 7725 ax-cnex 11166 ax-resscn 11167 ax-1cn 11168 ax-icn 11169 ax-addcl 11170 ax-addrcl 11171 ax-mulcl 11172 ax-mulrcl 11173 ax-mulcom 11174 ax-addass 11175 ax-mulass 11176 ax-distr 11177 ax-i2m1 11178 ax-1ne0 11179 ax-1rid 11180 ax-rnegex 11181 ax-rrecex 11182 ax-cnre 11183 ax-pre-lttri 11184 ax-pre-lttrn 11185 ax-pre-ltadd 11186 ax-pre-mulgt0 11187 |
| This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2942 df-nel 3048 df-ral 3063 df-rex 3072 df-rmo 3377 df-reu 3378 df-rab 3434 df-v 3477 df-sbc 3779 df-csb 3895 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-pss 3968 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4910 df-iun 5000 df-br 5150 df-opab 5212 df-mpt 5233 df-tr 5267 df-id 5575 df-eprel 5581 df-po 5589 df-so 5590 df-fr 5632 df-we 5634 df-xp 5683 df-rel 5684 df-cnv 5685 df-co 5686 df-dm 5687 df-rn 5688 df-res 5689 df-ima 5690 df-pred 6301 df-ord 6368 df-on 6369 df-lim 6370 df-suc 6371 df-iota 6496 df-fun 6546 df-fn 6547 df-f 6548 df-f1 6549 df-fo 6550 df-f1o 6551 df-fv 6552 df-riota 7365 df-ov 7412 df-oprab 7413 df-mpo 7414 df-om 7856 df-2nd 7976 df-frecs 8266 df-wrecs 8297 df-recs 8371 df-rdg 8410 df-er 8703 df-en 8940 df-dom 8941 df-sdom 8942 df-pnf 11250 df-mnf 11251 df-xr 11252 df-ltxr 11253 df-le 11254 df-sub 11446 df-neg 11447 df-nn 12213 df-2 12275
df-sets 17097 df-slot 17115 df-ndx 17127 df-base 17145 df-plusg 17210 df-0g 17387 df-mgm 18561 df-sgrp 18610 df-mnd 18626 df-grp 18822 df-minusg 18823 df-cmn 19650 df-abl 19651 df-mgp 19988 df-ur 20005 df-ring 20058 |
| This theorem is referenced by: ringsrg
20109 gsummulc1OLD
20126 gsummulc2OLD
20127 gsumfsum
21012 nn0srg
21015 rge0srg
21016 regsumsupp
21175 ip2di
21194 psrlidm
21523 psrridm
21524 psrdi
21526 psrdir
21527 psrcom
21529 mplmonmul
21591 mplcoe1
21592 evlslem2
21642 evlslem1
21645 evlsgsumadd
21654 mhpmulcl
21692 psropprmul
21760 coe1mul2
21791 coe1fzgsumdlem
21825 gsumsmonply1
21827 gsummoncoe1
21828 lply1binom
21830 evls1gsumadd
21843 evl1gsumdlem
21875 mamucl
21901 mamudi
21903 mamudir
21904 mat1dimmul
21978 dmatmul
21999 mavmulcl
22049 mdetleib2
22090 mdetf
22097 mdetrlin
22104 mdetralt
22110 m2detleib
22133 madugsum
22145 smadiadetlem3lem2
22169 smadiadet
22172 mat2pmatmul
22233 m2pmfzgsumcl
22250 decpmatmul
22274 pmatcollpw1
22278 pmatcollpwfi
22284 pmatcollpw3fi1lem1
22288 pm2mpcl
22299 mply1topmatcl
22307 mp2pm2mplem2
22309 mp2pm2mplem4
22311 mp2pm2mp
22313 pm2mpghm
22318 pm2mpmhmlem2
22321 pm2mp
22327 chfacfscmulgsum
22362 chfacfpmmulgsum
22366 cpmadugsumlemF
22378 cpmadugsumfi
22379 cayhamlem4
22390 tdeglem1
25573 tdeglem1OLD
25574 tdeglem3
25575 tdeglem3OLD
25576 tdeglem4
25577 tdeglem4OLD
25578 plypf1
25726 taylfvallem
25870 taylf
25873 tayl0
25874 taylpfval
25877 jensenlem1
26491 jensenlem2
26492 jensen
26493 amgm
26495 freshmansdream
32412 ofldchr
32463 elrspunidl
32577 ply1degltdimlem
32738 fedgmullem1
32745 fedgmullem2
32746 mdetpmtr1
32834 zarcmplem
32892 matunitlindflem1
36532 lfladdcl
37989 mhphflem
41216 ply1mulgsum
47119 amgmwlem
47897 |
