Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ↔ wb 205
∈ wcel 2107 ∀wral 3062 ‘cfv 6544
(class class class)co 7409 Basecbs 17144
+gcplusg 17197 SubGrpcsubg 19000 NrmSGrpcnsg 19001 |
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-pow 5364 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-ne 2942 df-ral 3063 df-rex 3072 df-rab 3434 df-v 3477 df-sbc 3779 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4910 df-br 5150 df-opab 5212 df-mpt 5233 df-id 5575 df-xp 5683 df-rel 5684 df-cnv 5685 df-co 5686 df-dm 5687 df-rn 5688 df-res 5689 df-ima 5690 df-iota 6496 df-fun 6546 df-fv 6552 df-ov 7412 df-subg 19003 df-nsg 19004 |
This theorem is referenced by: nsgconj
19039 isnsg3
19040 trivnsgd
19052 eqgcpbl
19062 qusgrp
19065 quseccl
19066 qusadd
19067 qus0
19068 qusinv
19069 qussub
19070 ghmnsgima
19116 ghmnsgpreima
19117 conjnsg
19128 qusghm
19129 sylow3lem4
19498 prmgrpsimpgd
19984 clsnsg
23614 qustgpopn
23624 qustgphaus
23627 cyc3genpm
32311 qusker
32464 qus0g
32518 qusima
32519 qusrn
32520 nsgqus0
32521 nsgmgclem
32522 nsgmgc
32523 nsgqusf1olem1
32524 nsgqusf1olem2
32525 nsgqusf1olem3
32526 ghmquskerlem1
32528 ghmquskerlem2
32530 ghmquskerlem3
32531 ghmqusker
32532 lmhmqusker
32534 rhmquskerlem
32543 qsnzr
32574 opprqusplusg
32603 opprqus0g
32604 qsdrngilem
32608 qsdrngi
32609 ecqusaddcl
46769 rngqiprngimf1lem
46779 rngqiprngimf1
46785 rngqiprngimfo
46786 rngqiprngfulem4
46799 rngqipring1
46801 |