Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 = wceq 1542
∈ wcel 2107 ⊆
wss 3911 ‘cfv 6497
SubGrpcsubg 18927 LModclmod 20336 LSubSpclss 20407 |
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 5257 ax-nul 5264 ax-pow 5321 ax-pr 5385 ax-un 7673 ax-cnex 11112 ax-resscn 11113 ax-1cn 11114 ax-icn 11115 ax-addcl 11116 ax-addrcl 11117 ax-mulcl 11118 ax-mulrcl 11119 ax-mulcom 11120 ax-addass 11121 ax-mulass 11122 ax-distr 11123 ax-i2m1 11124 ax-1ne0 11125 ax-1rid 11126 ax-rnegex 11127 ax-rrecex 11128 ax-cnre 11129 ax-pre-lttri 11130 ax-pre-lttrn 11131 ax-pre-ltadd 11132 ax-pre-mulgt0 11133 |
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 3446 df-sbc 3741 df-csb 3857 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-pss 3930 df-nul 4284 df-if 4488 df-pw 4563 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-iun 4957 df-br 5107 df-opab 5169 df-mpt 5190 df-tr 5224 df-id 5532 df-eprel 5538 df-po 5546 df-so 5547 df-fr 5589 df-we 5591 df-xp 5640 df-rel 5641 df-cnv 5642 df-co 5643 df-dm 5644 df-rn 5645 df-res 5646 df-ima 5647 df-pred 6254 df-ord 6321 df-on 6322 df-lim 6323 df-suc 6324 df-iota 6449 df-fun 6499 df-fn 6500 df-f 6501 df-f1 6502 df-fo 6503 df-f1o 6504 df-fv 6505 df-riota 7314 df-ov 7361 df-oprab 7362 df-mpo 7363 df-om 7804 df-1st 7922 df-2nd 7923 df-frecs 8213 df-wrecs 8244 df-recs 8318 df-rdg 8357 df-er 8651 df-en 8887 df-dom 8888 df-sdom 8889 df-pnf 11196 df-mnf 11197 df-xr 11198 df-ltxr 11199 df-le 11200 df-sub 11392 df-neg 11393 df-nn 12159 df-2 12221
df-sets 17041 df-slot 17059 df-ndx 17071 df-base 17089 df-ress 17118 df-plusg 17151 df-0g 17328 df-mgm 18502 df-sgrp 18551 df-mnd 18562 df-grp 18756 df-minusg 18757 df-sbg 18758 df-subg 18930 df-mgp 19902 df-ur 19919 df-ring 19971 df-lmod 20338 df-lss 20408 |
This theorem is referenced by: lsmsp
20562 lspprabs
20571 pj1lmhm
20576 pj1lmhm2
20577 lspindpi
20609 lvecindp
20615 lsmcv
20618 pjdm2
21133 pjf2
21136 pjfo
21137 ocvpj
21139 pjthlem2
24818 lshpnel
37491 lshpnelb
37492 lsmsat
37516 lrelat
37522 lsmcv2
37537 lcvexchlem1
37542 lcvexchlem2
37543 lcvexchlem3
37544 lcvexchlem4
37545 lcvexchlem5
37546 lcv1
37549 lcv2
37550 lsatexch
37551 lsatcv0eq
37555 lsatcvatlem
37557 lsatcvat
37558 lsatcvat3
37560 l1cvat
37563 lkrlsp
37610 lshpsmreu
37617 lshpkrlem5
37622 dia2dimlem5
39577 dia2dimlem9
39581 dvhopellsm
39626 diblsmopel
39680 cdlemn5pre
39709 cdlemn11c
39718 dihjustlem
39725 dihord1
39727 dihord2a
39728 dihord2b
39729 dihord11c
39733 dihord6apre
39765 dihord5b
39768 dihord5apre
39771 dihjatc3
39822 dihmeetlem9N
39824 dihjatcclem1
39927 dihjatcclem2
39928 dihjat
39932 dvh3dim3N
39958 dochexmidlem2
39970 dochexmidlem6
39974 dochexmidlem7
39975 lclkrlem2b
40017 lclkrlem2f
40021 lclkrlem2v
40037 lclkrslem2
40047 lcfrlem23
40074 lcfrlem25
40076 lcfrlem35
40086 mapdlsm
40173 mapdpglem3
40184 mapdindp0
40228 lspindp5
40279 hdmaprnlem3eN
40367 hdmapglem7a
40436 |