Intermediately automorph-conjugate of normal implies weakly pronormal

Property-theoretic statement
The subgroup property of being an intermediately automorph-conjugate subgroup of normal subgroup (i.e., the property obtained by applying the composition operator to the properties of intermediately automorph-conjugate subgroup and normal subgroup) is stronger than the subgroup property of being a weakly pronormal subgroup.

Verbal statement
Any fact about::intermediately automorph-conjugate subgroup of a fact about::normal subgroup of a group is weakly pronormal.

Weaker facts

 * Intermediately automorph-conjugate implies weakly pronormal

Corollaries

 * Frattini's argument

Similar facts

 * Intermediately isomorph-conjugate of normal implies pronormal
 * Intermediately normal-to-characteristic of normal implies intermediately subnormal-to-normal