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

theorem Th15:
  for x being Subset of FinSETS st x is finite holds x is Element of FinSETS
  proof
    let x be Subset of FinSETS;
    assume x is finite;
    then card x in omega by CARD_3:84;
    then card x in card FinSETS by CARD_3:def 15,CLASSES4:19;
    hence thesis by CLASSES1:1;
  end;
