Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ w3a 1088
= wceq 1542 ∈
wcel 2107 ‘cfv 6544
(class class class)co 7409 Basecbs 17144
Grpcgrp 18819 -gcsg 18821 LModclmod 20471 |
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 |
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-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-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-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-id 5575 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-iota 6496 df-fun 6546 df-fn 6547 df-f 6548 df-fv 6552 df-riota 7365 df-ov 7412 df-oprab 7413 df-mpo 7414 df-1st 7975 df-2nd 7976 df-0g 17387 df-mgm 18561 df-sgrp 18610 df-mnd 18626 df-grp 18822 df-minusg 18823 df-sbg 18824 df-lmod 20473 |
This theorem is referenced by: lspsnsub
20618 lvecvscan
20724 ip2subdi
21197 ip2eq
21206 ipcau2
24751 nmparlem
24756 minveclem1
24941 minveclem2
24943 minveclem4
24949 minveclem6
24951 pjthlem1
24954 pjthlem2
24955 eqlkr
37969 lkrlsp
37972 mapdpglem1
40543 mapdpglem2
40544 mapdpglem5N
40548 mapdpglem8
40550 mapdpglem9
40551 mapdpglem13
40555 mapdpglem14
40556 mapdpglem27
40570 baerlem3lem2
40581 baerlem5alem2
40582 baerlem5blem2
40583 mapdheq4lem
40602 mapdh6lem1N
40604 mapdh6lem2N
40605 hdmap1l6lem1
40678 hdmap1l6lem2
40679 hdmap11
40719 hdmapinvlem4
40792 |