reserve X for set;
reserve UN for Universe;

theorem
  for n being Element of FinSETS holds GrothendieckUniverse n = FinSETS
  proof
    let n be Element of FinSETS;
    FinSETS is Grothendieck of n by CLASSES3:def 4;
    hence thesis by Th45,CLASSES3:def 5;
  end;
