Paranormality is strongly join-closed

Statement
The join of an arbitrary (possibly empty) collection of paranormal subgroups of a group is again paranormal.

Related facts

 * Polynormality is strongly join-closed
 * Paracharacteristicity is strongly join-closed
 * Polycharacteristicity is strongly join-closed

Facts used

 * 1) Endomorphisms commute with joins
 * 2) Contranormality is UL-join-closed