Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ wa 397
= wceq 1542 ∈
wcel 2107 ∀wral 3065
‘cfv 6501 (class class class)co 7362
Basecbs 17090 +gcplusg 17140 .rcmulr 17141 Mndcmnd 18563
Grpcgrp 18755 mulGrpcmgp 19903 Ringcrg 19971 |
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-ext 2708 ax-nul 5268 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-sb 2069 df-clab 2715 df-cleq 2729 df-clel 2815 df-ne 2945 df-ral 3066 df-rab 3411 df-v 3450 df-sbc 3745 df-dif 3918 df-un 3920 df-in 3922 df-ss 3932 df-nul 4288 df-if 4492 df-sn 4592 df-pr 4594 df-op 4598 df-uni 4871 df-br 5111 df-iota 6453 df-fv 6509 df-ov 7365 df-ring 19973 |
This theorem is referenced by: mgpf
19986 ringcl
19988 iscrng2
19990 ringass
19991 ringideu
19992 ringidcl
19996 ringidmlem
19998 ringsrg
20020 pwspjmhmmgpd
20050 pwsexpg
20051 unitsubm
20106 dfrhm2
20157 isrhm2d
20169 idrhm
20172 pwsco1rhm
20181 pwsco2rhm
20182 subrgcrng
20242 subrgsubm
20251 issubrg3
20266 cntzsubr
20271 pwsdiagrhm
20272 subrgacs
20283 cnfldexp
20846 expmhm
20882 nn0srg
20883 rge0srg
20884 assamulgscmlem2
21319 psrcrng
21398 mplcoe3
21455 mplcoe5lem
21456 mplcoe5
21457 evlsgsummul
21518 mhppwdeg
21556 ply1moncl
21658 coe1pwmul
21666 ply1coefsupp
21682 ply1coe
21683 gsummoncoe1
21691 lply1binomsc
21694 evls1gsummul
21707 evl1expd
21727 evl1gsummul
21742 evl1scvarpw
21745 evl1scvarpwval
21746 evl1gsummon
21747 ringvcl
21763 mat1mhm
21849 scmatmhm
21899 m1detdiag
21962 mdetdiaglem
21963 m2detleiblem2
21993 mat2pmatmhm
22098 pmatcollpwscmatlem1
22154 mply1topmatcllem
22168 mply1topmatcl
22170 pm2mpghm
22181 pm2mpmhm
22185 monmat2matmon
22189 pm2mp
22190 chpscmatgsumbin
22209 chpscmatgsummon
22210 chfacfscmulcl
22222 chfacfscmul0
22223 chfacfpmmulcl
22226 chfacfpmmul0
22227 chfacfpmmulgsum2
22230 cayhamlem1
22231 cpmadugsumlemB
22239 cpmadugsumlemC
22240 cpmadugsumlemF
22241 cayhamlem2
22249 cayhamlem4
22253 nrgtrg
24070 deg1pw
25501 plypf1
25589 efsubm
25923 amgm
26356 wilthlem2
26434 wilthlem3
26435 dchrelbas3
26602 lgsqrlem2
26711 lgsqrlem3
26712 lgsqrlem4
26713 cntrcrng
31946 psgnid
31988 cnmsgn0g
32037 altgnsg
32040 freshmansdream
32109 frobrhm
32110 fermltlchr
32194 znfermltl
32195 ringlsmss
32216 evls1fpws
32311 iistmd
32523 evlsbagval
40777 evlsexpval
40778 mhphf
40800 hbtlem4
41482 idomrootle
41551 isdomn3
41560 mon1psubm
41562 amgm2d
42545 amgm3d
42546 amgm4d
42547 c0rhm
46284 c0rnghm
46285 lidlmsgrp
46298 invginvrid
46517 ply1mulgsumlem4
46544 ply1mulgsum
46545 amgmw2d
47325 |