Colors of
variables: wff
setvar class |
Syntax hints:
β wi 4 β§ wa 397
β wcel 2107 βwral 3061 {crab 3406
π« cpw 4561 βcfv 6497 (class class class)co 7358
Basecbs 17088 +gcplusg 17138 0gc0g 17326 Mndcmnd 18561
SubMndcsubmnd 18605 |
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-ral 3062 df-rex 3071 df-rab 3407 df-v 3446 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-xp 5640 df-rel 5641 df-cnv 5642 df-dm 5644 df-rn 5645 df-res 5646 df-ima 5647 df-iota 6449 df-fv 6505 df-submnd 18607 |
This theorem is referenced by: issubmndb
18621 submss
18625 subm0cl
18627 submcl
18628 submmnd
18629 subm0
18631 subsubm
18632 insubm
18634 resmhm2
18637 gsumsubm
18650 gsumwsubmcl
18652 submmulgcl
18924 oppgsubm
19148 lsmub1x
19433 lsmub2x
19434 lsmsubm
19440 submarchi
32071 |