Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ w3a 1087
= wceq 1541 ∈
wcel 2106 ‘cfv 6543
(class class class)co 7411 Basecbs 17146
Grpcgrp 18821 -gcsg 18823 LModclmod 20475 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913
ax-6 1971 ax-7 2011 ax-8 2108
ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2703 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7727 |
This theorem depends on definitions:
df-bi 206 df-an 397
df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2534 df-eu 2563 df-clab 2710 df-cleq 2724 df-clel 2810 df-nfc 2885 df-ne 2941 df-ral 3062 df-rex 3071 df-rmo 3376 df-reu 3377 df-rab 3433 df-v 3476 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-iun 4999 df-br 5149 df-opab 5211 df-mpt 5232 df-id 5574 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-fv 6551 df-riota 7367 df-ov 7414 df-oprab 7415 df-mpo 7416 df-1st 7977 df-2nd 7978 df-0g 17389 df-mgm 18563 df-sgrp 18612 df-mnd 18628 df-grp 18824 df-minusg 18825 df-sbg 18826 df-lmod 20477 |
This theorem is referenced by: lspsnsub
20623 lvecvscan
20730 ip2subdi
21203 ip2eq
21212 ipcau2
24758 nmparlem
24763 minveclem1
24948 minveclem2
24950 minveclem4
24956 minveclem6
24958 pjthlem1
24961 pjthlem2
24962 eqlkr
38055 lkrlsp
38058 mapdpglem1
40629 mapdpglem2
40630 mapdpglem5N
40634 mapdpglem8
40636 mapdpglem9
40637 mapdpglem13
40641 mapdpglem14
40642 mapdpglem27
40656 baerlem3lem2
40667 baerlem5alem2
40668 baerlem5blem2
40669 mapdheq4lem
40688 mapdh6lem1N
40690 mapdh6lem2N
40691 hdmap1l6lem1
40764 hdmap1l6lem2
40765 hdmap11
40805 hdmapinvlem4
40878 |