Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2107
∀wral 3061 {crab 3406
𝒫 cpw 4561 dom cdm 5634
‘cfv 6497 (class class class)co 7358
Basecbs 17088 +gcplusg 17138 Mgmcmgm 18500
SubMgmcsubmgm 46158 |
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-submgm 46160 |
This theorem is referenced by: submgmss
46172 submgmcl
46174 submgmmgm
46175 subsubmgm
46177 resmgmhm2
46179 |