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Definition df-slw 15175
 Description: Define the set of Sylow p-subgroups of a group . A Sylow p-subgroup is a p-group that is not a subgroup of any other p-groups in . (Contributed by Mario Carneiro, 16-Jan-2015.)
Assertion
Ref Expression
df-slw pSyl SubGrp SubGrp pGrp s
Distinct variable group:   ,,,

Detailed syntax breakdown of Definition df-slw
StepHypRef Expression
1 cslw 15171 . 2 pSyl
2 vp . . 3
3 vg . . 3
4 cprime 13084 . . 3
5 cgrp 14690 . . 3
6 vh . . . . . . . . 9
76cv 1652 . . . . . . . 8
8 vk . . . . . . . . 9
98cv 1652 . . . . . . . 8
107, 9wss 3322 . . . . . . 7
112cv 1652 . . . . . . . 8
123cv 1652 . . . . . . . . 9
13 cress 13475 . . . . . . . . 9 s
1412, 9, 13co 6084 . . . . . . . 8 s
15 cpgp 15170 . . . . . . . 8 pGrp
1611, 14, 15wbr 4215 . . . . . . 7 pGrp s
1710, 16wa 360 . . . . . 6 pGrp s
186, 8weq 1654 . . . . . 6
1917, 18wb 178 . . . . 5 pGrp s
20 csubg 14943 . . . . . 6 SubGrp
2112, 20cfv 5457 . . . . 5 SubGrp
2219, 8, 21wral 2707 . . . 4 SubGrp pGrp s
2322, 6, 21crab 2711 . . 3 SubGrp SubGrp pGrp s
242, 3, 4, 5, 23cmpt2 6086 . 2 SubGrp SubGrp pGrp s
251, 24wceq 1653 1 pSyl SubGrp SubGrp pGrp s
 Colors of variables: wff set class This definition is referenced by:  isslw  15247
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