reserve U for Universe;
reserve x for Element of U;
reserve U1,U2 for Universe;

theorem
  for X being class of U holds union X is class of U
  proof
    let X be class of U;
A1: union X is non empty
    proof
      assume union X is empty;
      then
A2:   X is U-set by Th45;
      X is U-Class by Def12;
      hence thesis by A2;
    end;
A3: X is U-Class by Def12;
    then union X c= union U by ZFMISC_1:77;
    then union X c= U & not union X in U by A3,Th21,CLASSES4:81;
    then union X is U-Class;
    hence thesis by A1,Def12;
  end;
