Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2098
∀wral 3055 {crab 3426
𝒫 cpw 4597 dom cdm 5669
‘cfv 6537 (class class class)co 7405
Basecbs 17153 +gcplusg 17206 Mgmcmgm 18571
SubMgmcsubmgm 18624 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905
ax-6 1963 ax-7 2003 ax-8 2100
ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2163 ax-ext 2697 ax-sep 5292 ax-nul 5299 ax-pr 5420 |
This theorem depends on definitions:
df-bi 206 df-an 396
df-or 845 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2704 df-cleq 2718 df-clel 2804 df-nfc 2879 df-ral 3056 df-rex 3065 df-rab 3427 df-v 3470 df-dif 3946 df-un 3948 df-in 3950 df-ss 3960 df-nul 4318 df-if 4524 df-sn 4624 df-pr 4626 df-op 4630 df-uni 4903 df-br 5142 df-opab 5204 df-mpt 5225 df-xp 5675 df-rel 5676 df-cnv 5677 df-dm 5679 df-rn 5680 df-res 5681 df-ima 5682 df-iota 6489 df-fv 6545 df-submgm 18626 |
This theorem is referenced by: submgmss
18638 submgmcl
18640 submgmmgm
18641 subsubmgm
18643 resmgmhm2
18645 |