Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 = wceq 1542
∈ wcel 2107 ⊆
wss 3914 ‘cfv 6500
(class class class)co 7361 Basecbs 17091
↾s cress 17120 SubGrpcsubg 18930 |
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 5260 ax-nul 5267 ax-pow 5324 ax-pr 5388 ax-un 7676 ax-cnex 11115 ax-1cn 11117 ax-addcl 11119 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3or 1089 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-reu 3353 df-rab 3407 df-v 3449 df-sbc 3744 df-csb 3860 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-pss 3933 df-nul 4287 df-if 4491 df-pw 4566 df-sn 4591 df-pr 4593 df-op 4597 df-uni 4870 df-iun 4960 df-br 5110 df-opab 5172 df-mpt 5193 df-tr 5227 df-id 5535 df-eprel 5541 df-po 5549 df-so 5550 df-fr 5592 df-we 5594 df-xp 5643 df-rel 5644 df-cnv 5645 df-co 5646 df-dm 5647 df-rn 5648 df-res 5649 df-ima 5650 df-pred 6257 df-ord 6324 df-on 6325 df-lim 6326 df-suc 6327 df-iota 6452 df-fun 6502 df-fn 6503 df-f 6504 df-f1 6505 df-fo 6506 df-f1o 6507 df-fv 6508 df-ov 7364 df-oprab 7365 df-mpo 7366 df-om 7807 df-2nd 7926 df-frecs 8216 df-wrecs 8247 df-recs 8321 df-rdg 8360 df-nn 12162 df-sets 17044 df-slot 17062 df-ndx 17074 df-base 17092 df-ress 17121 df-subg 18933 |
This theorem is referenced by: subg0
18942 subginv
18943 subg0cl
18944 subginvcl
18945 subgcl
18946 subgsub
18948 subgmulg
18950 issubg2
18951 subsubg
18959 nmznsg
18978 subgga
19088 gasubg
19090 odsubdvds
19361 pgp0
19386 subgpgp
19387 sylow2blem2
19411 sylow2blem3
19412 slwhash
19414 fislw
19415 sylow3lem4
19420 sylow3lem6
19422 subglsm
19463 pj1ghm
19493 subgabl
19622 cycsubgcyg
19686 subgdmdprd
19821 ablfacrplem
19852 ablfac1c
19858 pgpfaclem1
19868 pgpfaclem2
19869 pgpfaclem3
19870 ablfaclem3
19874 ablfac2
19876 subrgbas
20273 issubrg2
20284 pj1lmhm
20605 phssip
21085 scmatsgrp1
21894 subgtgp
23479 subgnm
24012 subgngp
24014 lssnlm
24088 cmscsscms
24760 cssbn
24762 reefgim
25832 efabl
25929 |