Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ↔ wb 205
∧ wa 396 = wceq 1540
∈ wcel 2105 ∀wral 3061 ⊆ wss 3898
class class class wbr 5092 ‘cfv 6479
(class class class)co 7337 ℙcprime 16473 ↾s
cress 17038 SubGrpcsubg 18845 pGrp cpgp 19230
pSyl cslw 19231 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912
ax-6 1970 ax-7 2010 ax-8 2107
ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2707 ax-sep 5243 ax-nul 5250 ax-pow 5308 ax-pr 5372 |
This theorem depends on definitions:
df-bi 206 df-an 397
df-or 845 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-nf 1785 df-sb 2067 df-mo 2538 df-eu 2567 df-clab 2714 df-cleq 2728 df-clel 2814 df-nfc 2886 df-ne 2941 df-ral 3062 df-rex 3071 df-rab 3404 df-v 3443 df-sbc 3728 df-dif 3901 df-un 3903 df-in 3905 df-ss 3915 df-nul 4270 df-if 4474 df-pw 4549 df-sn 4574 df-pr 4576 df-op 4580 df-uni 4853 df-br 5093 df-opab 5155 df-mpt 5176 df-id 5518 df-xp 5626 df-rel 5627 df-cnv 5628 df-co 5629 df-dm 5630 df-rn 5631 df-res 5632 df-ima 5633 df-iota 6431 df-fun 6481 df-fv 6487 df-ov 7340 df-oprab 7341 df-mpo 7342 df-subg 18848 df-slw 19235 |
This theorem is referenced by: slwpgp
19314 subgslw
19317 slwhash
19325 fislw
19326 sylow2
19327 sylow3lem1
19328 sylow3lem2
19329 sylow3lem3
19330 sylow3lem4
19331 sylow3lem5
19332 sylow3lem6
19333 |