Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ wa 397
= wceq 1542 ∈
wcel 2107 ‘cfv 6497
(class class class)co 7358 Basecbs 17088
+gcplusg 17138 0gc0g 17326 Mndcmnd 18561 |
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-pr 5385 |
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 2941 df-ral 3062 df-rex 3071 df-rmo 3352 df-reu 3353 df-rab 3407 df-v 3446 df-sbc 3741 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-nul 4284 df-if 4488 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-br 5107 df-opab 5169 df-mpt 5190 df-id 5532 df-xp 5640 df-rel 5641 df-cnv 5642 df-co 5643 df-dm 5644 df-iota 6449 df-fun 6499 df-fv 6505 df-riota 7314 df-ov 7361 df-0g 17328 df-mgm 18502 df-sgrp 18551 df-mnd 18562 |
This theorem is referenced by: issubmnd
18588 ress0g
18589 submnd0
18590 mndinvmod
18591 prdsidlem
18593 imasmnd
18599 0subm
18633 0mhm
18635 mndind
18643 gsumccat
18656 dfgrp2
18780 grplid
18785 dfgrp3
18851 mhmid
18873 mhmmnd
18874 mulgnn0p1
18892 mulgnn0z
18908 mulgnn0dir
18911 cntzsubm
19121 oppgmnd
19140 odmodnn0
19327 lsmub2x
19434 mulgnn0di
19609 gsumval3
19689 gsumzaddlem
19703 gsumzsplit
19709 srgbinomlem4
19965 dsmmacl
21163 mndvlid
21758 dmatmul
21862 mndifsplit
22001 tsmssplit
23519 cntzsnid
31952 omndmul2
31969 omndmul3
31970 slmd0vlid
32106 c0mgm
46293 c0mhm
46294 c0snmgmhm
46298 cznrng
46339 mndpsuppss
46533 mndtccatid
47199 |