theorem Th19:
  X in W implies sup X in W
proof
  reconsider a = union On X as Ordinal by ORDINAL3:5;
A1: On X c= X by ORDINAL2:7;
  assume X in W;
  then On X in W by A1,CLASSES1:def 1;
  then reconsider a as Ordinal of W by CLASSES2:59;
  sup X c= succ a by ORDINAL3:72;
  hence thesis by CLASSES1:def 1;
end;
