Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 = wceq 1542
∈ wcel 2107 ⊆
wss 3949 ‘cfv 6544
(class class class)co 7409 Basecbs 17144
↾s cress 17173 Grpcgrp 18819
SubGrpcsubg 19000 |
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-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 |
This theorem is referenced by: subg0
19012 subginv
19013 subg0cl
19014 subginvcl
19015 subgcl
19016 issubg2
19021 issubgrpd
19023 subsubg
19029 resghm
19108 resghm2b
19110 subgga
19164 gasubg
19166 odsubdvds
19439 pgp0
19464 subgpgp
19465 sylow2blem2
19489 slwhash
19492 fislw
19493 subglsm
19541 pj1ghm
19571 subgabl
19704 cntrabl
19711 cycsubgcyg
19769 subgdmdprd
19904 subgdprd
19905 ablfacrplem
19935 pgpfaclem1
19951 pgpfaclem3
19953 ablfaclem3
19957 issubrg2
20339 subdrgint
20419 islss3
20570 zringcyg
21039 cnmsgngrp
21132 psgnghm
21133 mplgrp
21576 scmatghm
22035 subgtgp
23609 subgngp
24144 reefgim
25962 ressply1sub
32659 amgmlemALT
47850 |