thus SubAlgCl MA is absolutely-multiplicative :: thesis: verum

proof

reconsider SF = SubSort MA as absolutely-multiplicative SubsetFamily of the Sorts of MA by Th13;
set F = the Family of (SubAlgCl MA);
( the Sorts of (SubAlgCl MA) = the Sorts of MA & the Family of (SubAlgCl MA) = SF ) by Def5;
hence SubAlgCl MA is absolutely-multiplicative ; :: thesis: verum

end;