 reserve x,y,X,Y for set;
reserve G for non empty multMagma,
  D for set,
  a,b,c,r,l for Element of G;
reserve M for non empty multLoopStr;
reserve H for non empty SubStr of G,
  N for non empty MonoidalSubStr of G;

theorem
  1 is_a_unity_wrt multnat & multnat is uniquely-decomposable
proof
  ex n being Element of NAT st n is_a_unity_wrt multnat by SETWISEO:def 2;
  hence 1 is_a_unity_wrt multnat by Th52,Th54,BINOP_1:def 8;
  thus thesis by Def20,Th52;
end;
