Metabelian implies subnormal join property

Statement
A metabelian group satisfies the group satisfying subnormal join property: the join of any two fact about::subnormal subgroups of the group is subnormal.

Facts used

 * 1) uses::Metabelian implies nilpotent commutator subgroup
 * 2) uses::Nilpotent commutator subgroup implies subnormal join property

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