Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 = wceq 1542
∈ wcel 2107 ⊆
wss 3911 ‘cfv 6497
(class class class)co 7358 Basecbs 17088
↾s cress 17117 Grpcgrp 18753
SubGrpcsubg 18927 |
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-pow 5321 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-ne 2941 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-pw 4563 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-br 5107 df-opab 5169 df-mpt 5190 df-id 5532 df-xp 5640 df-rel 5641 df-cnv 5642 df-co 5643 df-dm 5644 df-rn 5645 df-res 5646 df-ima 5647 df-iota 6449 df-fun 6499 df-fv 6505 df-ov 7361 df-subg 18930 |
This theorem is referenced by: subg0
18939 subginv
18940 subg0cl
18941 subginvcl
18942 subgcl
18943 issubg2
18948 issubgrpd
18950 subsubg
18956 resghm
19029 resghm2b
19031 subgga
19085 gasubg
19087 odsubdvds
19358 pgp0
19383 subgpgp
19384 sylow2blem2
19408 slwhash
19411 fislw
19412 subglsm
19460 pj1ghm
19490 subgabl
19619 cntrabl
19626 cycsubgcyg
19683 subgdmdprd
19818 subgdprd
19819 ablfacrplem
19849 pgpfaclem1
19865 pgpfaclem3
19867 ablfaclem3
19871 issubrg2
20256 subdrgint
20284 islss3
20435 zringcyg
20906 cnmsgngrp
20999 psgnghm
21000 mplgrp
21438 scmatghm
21898 subgtgp
23472 subgngp
24007 reefgim
25825 ressply1sub
32329 amgmlemALT
47336 |