2-subnormality is conjugate-join-closed

Statement
A join of any collection of 2-subnormal subgroups that are conjugate to each other is also a 2-subnormal subgroup.

Related facts

 * Weaker than in assumption and conclusion::Normality is strongly join-closed: An arbitrary join of normal subgroups is normal.
 * Subnormality is normalizing join-closed
 * Stronger than in assumption and conclusion::3-subnormal implies finite-conjugate-join-closed subnormal