Sylow of normal implies pronormal

This article gives the statement and possibly, proof, of an implication relation between two subgroup properties, when the big group is a finite group. That is, it states that in a Finite group (?), every subgroup satisfying the first subgroup property (i.e., Sylow subgroup of normal subgroup (?)) must also satisfy the second subgroup property (i.e., Pronormal subgroup (?)). In other words, every Sylow subgroup of normal subgroup of finite group is a pronormal subgroup of finite group.
View all subgroup property implications in finite groups

$|$

View all subgroup property non-implications in finite groups

$|$

View all subgroup property implications

$|$

View all subgroup property non-implications

Statement

Any Sylow subgroup of a normal subgroup of a group is pronormal.

Facts used

1. Sylow implies intermediately isomorph-conjugate
2. Intermediately isomorph-conjugate of normal implies pronormal

Proof

The proof follows directly by combining facts (1) and (2).