reserve U for Universe;
reserve x for Element of U;

theorem
  for x being Subset of FinSETS st x is finite holds x is Set of FinSETS
  proof
    let x be Subset of FinSETS;
    assume x is finite;
    then x is Element of FinSETS by Th15;
    then x is FinSETS-set;
    hence thesis by Def10;
  end;
