Pronormal implies MWNSCDIN

This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., pronormal subgroup) must also satisfy the second subgroup property (i.e., MWNSCDIN-subgroup)
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Statement

Any pronormal subgroup of a group is a MWNSCDIN-subgroup.

Proof

The proof is an adaptation of the proof of pronormal implies WNSCDIN. Instead of using the normalizer of just the one image set, we use the intersection of the normalizers of all the image sets. The rest of the proof is identical.