Colors of
variables: wff
setvar class |
Syntax hints:
β wi 4 β§ wa 397
β wcel 2107 βwral 3062 {crab 3433
π« cpw 4603 βcfv 6544 (class class class)co 7409
Basecbs 17144 +gcplusg 17197 0gc0g 17385 Mndcmnd 18625
SubMndcsubmnd 18670 |
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-pr 5428 |
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-ral 3063 df-rex 3072 df-rab 3434 df-v 3477 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-nul 4324 df-if 4530 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4910 df-br 5150 df-opab 5212 df-mpt 5233 df-xp 5683 df-rel 5684 df-cnv 5685 df-dm 5687 df-rn 5688 df-res 5689 df-ima 5690 df-iota 6496 df-fv 6552 df-submnd 18672 |
This theorem is referenced by: issubmndb
18686 submss
18690 subm0cl
18692 submcl
18693 submmnd
18694 subm0
18696 subsubm
18697 insubm
18699 resmhm2
18702 gsumsubm
18716 gsumwsubmcl
18718 submmulgcl
18997 oppgsubm
19229 lsmub1x
19514 lsmub2x
19515 lsmsubm
19521 submarchi
32332 |