| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 = wceq 1542
∈ wcel 2107 ⊆
wss 3949 ‘cfv 6544
SubGrpcsubg 19000 LModclmod 20471 LSubSpclss 20542 |
| 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-1st 7975 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-ress 17174 df-plusg 17210 df-0g 17387 df-mgm 18561 df-sgrp 18610 df-mnd 18626 df-grp 18822 df-minusg 18823 df-sbg 18824 df-subg 19003 df-mgp 19988 df-ur 20005 df-ring 20058 df-lmod 20473 df-lss 20543 |
| This theorem is referenced by: lsmsp
20697 lspprabs
20706 pj1lmhm
20711 pj1lmhm2
20712 lspindpi
20745 lvecindp
20751 lsmcv
20754 pjdm2
21266 pjf2
21269 pjfo
21270 ocvpj
21272 pjthlem2
24955 lshpnel
37853 lshpnelb
37854 lsmsat
37878 lrelat
37884 lsmcv2
37899 lcvexchlem1
37904 lcvexchlem2
37905 lcvexchlem3
37906 lcvexchlem4
37907 lcvexchlem5
37908 lcv1
37911 lcv2
37912 lsatexch
37913 lsatcv0eq
37917 lsatcvatlem
37919 lsatcvat
37920 lsatcvat3
37922 l1cvat
37925 lkrlsp
37972 lshpsmreu
37979 lshpkrlem5
37984 dia2dimlem5
39939 dia2dimlem9
39943 dvhopellsm
39988 diblsmopel
40042 cdlemn5pre
40071 cdlemn11c
40080 dihjustlem
40087 dihord1
40089 dihord2a
40090 dihord2b
40091 dihord11c
40095 dihord6apre
40127 dihord5b
40130 dihord5apre
40133 dihjatc3
40184 dihmeetlem9N
40186 dihjatcclem1
40289 dihjatcclem2
40290 dihjat
40294 dvh3dim3N
40320 dochexmidlem2
40332 dochexmidlem6
40336 dochexmidlem7
40337 lclkrlem2b
40379 lclkrlem2f
40383 lclkrlem2v
40399 lclkrslem2
40409 lcfrlem23
40436 lcfrlem25
40438 lcfrlem35
40448 mapdlsm
40535 mapdpglem3
40546 mapdindp0
40590 lspindp5
40641 hdmaprnlem3eN
40729 hdmapglem7a
40798 |
