Metamath Proof Explorer


Theorem slwprm

Description: Reverse closure for the first argument of a Sylow P -subgroup. (Contributed by Mario Carneiro, 16-Jan-2015) (Revised by Mario Carneiro, 2-May-2015)

Ref Expression
Assertion slwprm H P pSyl G P

Proof

Step Hyp Ref Expression
1 isslw H P pSyl G P H SubGrp G k SubGrp G H k P pGrp G 𝑠 k H = k
2 1 simp1bi H P pSyl G P