Colors of
variables: wff
setvar class |
Syntax hints:
β wi 4 = wceq 1542
β wcel 2107 βcfv 6501 (class class class)co 7362
ndxcnx 17072 Basecbs 17090
βΎs cress 17119 .rcmulr 17141 |
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 2708 ax-sep 5261 ax-nul 5268 ax-pow 5325 ax-pr 5389 ax-un 7677 ax-cnex 11114 ax-resscn 11115 ax-1cn 11116 ax-icn 11117 ax-addcl 11118 ax-addrcl 11119 ax-mulcl 11120 ax-mulrcl 11121 ax-mulcom 11122 ax-addass 11123 ax-mulass 11124 ax-distr 11125 ax-i2m1 11126 ax-1ne0 11127 ax-1rid 11128 ax-rnegex 11129 ax-rrecex 11130 ax-cnre 11131 ax-pre-lttri 11132 ax-pre-lttrn 11133 ax-pre-ltadd 11134 ax-pre-mulgt0 11135 |
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 2539 df-eu 2568 df-clab 2715 df-cleq 2729 df-clel 2815 df-nfc 2890 df-ne 2945 df-nel 3051 df-ral 3066 df-rex 3075 df-reu 3357 df-rab 3411 df-v 3450 df-sbc 3745 df-csb 3861 df-dif 3918 df-un 3920 df-in 3922 df-ss 3932 df-pss 3934 df-nul 4288 df-if 4492 df-pw 4567 df-sn 4592 df-pr 4594 df-op 4598 df-uni 4871 df-iun 4961 df-br 5111 df-opab 5173 df-mpt 5194 df-tr 5228 df-id 5536 df-eprel 5542 df-po 5550 df-so 5551 df-fr 5593 df-we 5595 df-xp 5644 df-rel 5645 df-cnv 5646 df-co 5647 df-dm 5648 df-rn 5649 df-res 5650 df-ima 5651 df-pred 6258 df-ord 6325 df-on 6326 df-lim 6327 df-suc 6328 df-iota 6453 df-fun 6503 df-fn 6504 df-f 6505 df-f1 6506 df-fo 6507 df-f1o 6508 df-fv 6509 df-riota 7318 df-ov 7365 df-oprab 7366 df-mpo 7367 df-om 7808 df-2nd 7927 df-frecs 8217 df-wrecs 8248 df-recs 8322 df-rdg 8361 df-er 8655 df-en 8891 df-dom 8892 df-sdom 8893 df-pnf 11198 df-mnf 11199 df-xr 11200 df-ltxr 11201 df-le 11202 df-sub 11394 df-neg 11395 df-nn 12161 df-2 12223
df-3 12224 df-sets 17043 df-slot 17061 df-ndx 17073 df-base 17091 df-ress 17120 df-mulr 17154 |
This theorem is referenced by: mgpress
19918 mgpressOLD
19919 rdivmuldivd
20131 subrg1
20248 subrgmcl
20250 subrgdvds
20252 subrguss
20253 subrginv
20254 subrgdv
20255 subrgunit
20256 subrgugrp
20257 issubrg2
20258 subrgpropd
20273 primefld
20288 abvres
20314 sralmod
20672 nn0srg
20883 rge0srg
20884 zringmulr
20894 remulr
21031 issubassa3
21287 resspsrmul
21402 resspsrvsca
21403 mplmul
21431 ressmplmul
21447 mplmulr
21608 ply1mulr
21614 ressply1mul
21618 dmatcrng
21867 scmatcrng
21886 scmatsrng1
21888 scmatmhm
21899 clmmul
24454 isclmp
24476 cphsubrglem
24557 ipcau2
24614 qabvexp
26990 ostthlem2
26992 padicabv
26994 ostth2lem2
26998 ostth3
27002 ress1r
32111 suborng
32150 xrge0slmod
32180 idlinsubrg
32245 evls1muld
32314 drgextlsp
32335 fedgmullem1
32364 fedgmullem2
32365 extdg1id
32392 xrge0iifmhm
32560 qqhrhm
32610 imacrhmcl
40724 mhphf
40800 cnfldsrngmul
46139 lidlmmgm
46297 lidlmsgrp
46298 lidlrng
46299 zlidlring
46300 uzlidlring
46301 aacllem
47322 |