| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 = wceq 1539
∈ wcel 2104 ⊆
wss 3947 ‘cfv 6542
SubGrpcsubg 19036 LModclmod 20614 LSubSpclss 20686 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1911
ax-6 1969 ax-7 2009 ax-8 2106
ax-9 2114 ax-10 2135 ax-11 2152 ax-12 2169 ax-ext 2701 ax-sep 5298 ax-nul 5305 ax-pow 5362 ax-pr 5426 ax-un 7727 ax-cnex 11168 ax-resscn 11169 ax-1cn 11170 ax-icn 11171 ax-addcl 11172 ax-addrcl 11173 ax-mulcl 11174 ax-mulrcl 11175 ax-mulcom 11176 ax-addass 11177 ax-mulass 11178 ax-distr 11179 ax-i2m1 11180 ax-1ne0 11181 ax-1rid 11182 ax-rnegex 11183 ax-rrecex 11184 ax-cnre 11185 ax-pre-lttri 11186 ax-pre-lttrn 11187 ax-pre-ltadd 11188 ax-pre-mulgt0 11189 |
| This theorem depends on definitions:
df-bi 206 df-an 395
df-or 844 df-3or 1086 df-3an 1087 df-tru 1542 df-fal 1552 df-ex 1780 df-nf 1784 df-sb 2066 df-mo 2532 df-eu 2561 df-clab 2708 df-cleq 2722 df-clel 2808 df-nfc 2883 df-ne 2939 df-nel 3045 df-ral 3060 df-rex 3069 df-rmo 3374 df-reu 3375 df-rab 3431 df-v 3474 df-sbc 3777 df-csb 3893 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-pss 3966 df-nul 4322 df-if 4528 df-pw 4603 df-sn 4628 df-pr 4630 df-op 4634 df-uni 4908 df-iun 4998 df-br 5148 df-opab 5210 df-mpt 5231 df-tr 5265 df-id 5573 df-eprel 5579 df-po 5587 df-so 5588 df-fr 5630 df-we 5632 df-xp 5681 df-rel 5682 df-cnv 5683 df-co 5684 df-dm 5685 df-rn 5686 df-res 5687 df-ima 5688 df-pred 6299 df-ord 6366 df-on 6367 df-lim 6368 df-suc 6369 df-iota 6494 df-fun 6544 df-fn 6545 df-f 6546 df-f1 6547 df-fo 6548 df-f1o 6549 df-fv 6550 df-riota 7367 df-ov 7414 df-oprab 7415 df-mpo 7416 df-om 7858 df-1st 7977 df-2nd 7978 df-frecs 8268 df-wrecs 8299 df-recs 8373 df-rdg 8412 df-er 8705 df-en 8942 df-dom 8943 df-sdom 8944 df-pnf 11254 df-mnf 11255 df-xr 11256 df-ltxr 11257 df-le 11258 df-sub 11450 df-neg 11451 df-nn 12217 df-2 12279
df-sets 17101 df-slot 17119 df-ndx 17131 df-base 17149 df-ress 17178 df-plusg 17214 df-0g 17391 df-mgm 18565 df-sgrp 18644 df-mnd 18660 df-grp 18858 df-minusg 18859 df-sbg 18860 df-subg 19039 df-mgp 20029 df-ur 20076 df-ring 20129 df-lmod 20616 df-lss 20687 |
| This theorem is referenced by: lsmsp
20841 lspprabs
20850 pj1lmhm
20855 pj1lmhm2
20856 lspindpi
20890 lvecindp
20896 lsmcv
20899 pjdm2
21485 pjf2
21488 pjfo
21489 ocvpj
21491 pjthlem2
25186 lshpnel
38156 lshpnelb
38157 lsmsat
38181 lrelat
38187 lsmcv2
38202 lcvexchlem1
38207 lcvexchlem2
38208 lcvexchlem3
38209 lcvexchlem4
38210 lcvexchlem5
38211 lcv1
38214 lcv2
38215 lsatexch
38216 lsatcv0eq
38220 lsatcvatlem
38222 lsatcvat
38223 lsatcvat3
38225 l1cvat
38228 lkrlsp
38275 lshpsmreu
38282 lshpkrlem5
38287 dia2dimlem5
40242 dia2dimlem9
40246 dvhopellsm
40291 diblsmopel
40345 cdlemn5pre
40374 cdlemn11c
40383 dihjustlem
40390 dihord1
40392 dihord2a
40393 dihord2b
40394 dihord11c
40398 dihord6apre
40430 dihord5b
40433 dihord5apre
40436 dihjatc3
40487 dihmeetlem9N
40489 dihjatcclem1
40592 dihjatcclem2
40593 dihjat
40597 dvh3dim3N
40623 dochexmidlem2
40635 dochexmidlem6
40639 dochexmidlem7
40640 lclkrlem2b
40682 lclkrlem2f
40686 lclkrlem2v
40702 lclkrslem2
40712 lcfrlem23
40739 lcfrlem25
40741 lcfrlem35
40751 mapdlsm
40838 mapdpglem3
40849 mapdindp0
40893 lspindp5
40944 hdmaprnlem3eN
41032 hdmapglem7a
41101 |
