Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2107
CMndccmn 19570 Abelcabl 19571
Ringcrg 19972 |
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 5260 ax-nul 5267 ax-pow 5324 ax-pr 5388 ax-un 7676 ax-cnex 11115 ax-resscn 11116 ax-1cn 11117 ax-icn 11118 ax-addcl 11119 ax-addrcl 11120 ax-mulcl 11121 ax-mulrcl 11122 ax-mulcom 11123 ax-addass 11124 ax-mulass 11125 ax-distr 11126 ax-i2m1 11127 ax-1ne0 11128 ax-1rid 11129 ax-rnegex 11130 ax-rrecex 11131 ax-cnre 11132 ax-pre-lttri 11133 ax-pre-lttrn 11134 ax-pre-ltadd 11135 ax-pre-mulgt0 11136 |
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 2941 df-nel 3047 df-ral 3062 df-rex 3071 df-rmo 3352 df-reu 3353 df-rab 3407 df-v 3449 df-sbc 3744 df-csb 3860 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-pss 3933 df-nul 4287 df-if 4491 df-pw 4566 df-sn 4591 df-pr 4593 df-op 4597 df-uni 4870 df-iun 4960 df-br 5110 df-opab 5172 df-mpt 5193 df-tr 5227 df-id 5535 df-eprel 5541 df-po 5549 df-so 5550 df-fr 5592 df-we 5594 df-xp 5643 df-rel 5644 df-cnv 5645 df-co 5646 df-dm 5647 df-rn 5648 df-res 5649 df-ima 5650 df-pred 6257 df-ord 6324 df-on 6325 df-lim 6326 df-suc 6327 df-iota 6452 df-fun 6502 df-fn 6503 df-f 6504 df-f1 6505 df-fo 6506 df-f1o 6507 df-fv 6508 df-riota 7317 df-ov 7364 df-oprab 7365 df-mpo 7366 df-om 7807 df-2nd 7926 df-frecs 8216 df-wrecs 8247 df-recs 8321 df-rdg 8360 df-er 8654 df-en 8890 df-dom 8891 df-sdom 8892 df-pnf 11199 df-mnf 11200 df-xr 11201 df-ltxr 11202 df-le 11203 df-sub 11395 df-neg 11396 df-nn 12162 df-2 12224
df-sets 17044 df-slot 17062 df-ndx 17074 df-base 17092 df-plusg 17154 df-0g 17331 df-mgm 18505 df-sgrp 18554 df-mnd 18565 df-grp 18759 df-minusg 18760 df-cmn 19572 df-abl 19573 df-mgp 19905 df-ur 19922 df-ring 19974 |
This theorem is referenced by: ringsrg
20021 gsummulc1
20038 gsummulc2
20039 gsumdixp
20041 gsumfsum
20887 nn0srg
20890 rge0srg
20891 regsumsupp
21049 ip2di
21068 frlmphl
21210 psrlidm
21395 psrridm
21396 psrass1
21397 psrdi
21398 psrdir
21399 psrcom
21401 mplmonmul
21460 mplcoe1
21461 evlslem2
21512 evlslem1
21515 evlsgsumadd
21524 mhpmulcl
21562 psropprmul
21632 coe1mul2
21663 coe1fzgsumdlem
21695 gsumsmonply1
21697 gsummoncoe1
21698 lply1binom
21700 evls1gsumadd
21713 evl1gsumdlem
21745 mamucl
21771 mamuass
21772 mamudi
21773 mamudir
21774 mat1dimmul
21848 dmatmul
21869 mavmulcl
21919 mavmulass
21921 mdetleib2
21960 mdetf
21967 mdetrlin
21974 mdetralt
21980 m2detleib
22003 madugsum
22015 smadiadetlem3lem2
22039 smadiadet
22042 mat2pmatmul
22103 m2pmfzgsumcl
22120 decpmatmul
22144 pmatcollpw1
22148 pmatcollpwfi
22154 pmatcollpw3fi1lem1
22158 pm2mpcl
22169 mply1topmatcl
22177 mp2pm2mplem2
22179 mp2pm2mplem4
22181 mp2pm2mp
22183 pm2mpghm
22188 pm2mpmhmlem2
22191 pm2mp
22197 chfacfscmulgsum
22232 chfacfpmmulgsum
22236 cpmadugsumlemF
22248 cpmadugsumfi
22249 cayhamlem4
22260 tdeglem1
25443 tdeglem1OLD
25444 tdeglem3
25445 tdeglem3OLD
25446 tdeglem4
25447 tdeglem4OLD
25448 plypf1
25596 taylfvallem
25740 taylf
25743 tayl0
25744 taylpfval
25747 jensenlem1
26359 jensenlem2
26360 jensen
26361 amgm
26363 freshmansdream
32123 ofldchr
32163 elrspunidl
32258 ply1degltdimlem
32381 fedgmullem1
32388 fedgmullem2
32389 mdetpmtr1
32468 zarcmplem
32526 matunitlindflem1
36124 lfladdcl
37583 mhphflem
40817 ply1mulgsum
46561 amgmwlem
47339 |