reserve A,A1,A2,B,C,D for Ordinal,
  X,Y for set,
  x,y,a,b,c for object,
  L,L1,L2,L3 for Sequence,
  f for Function;

theorem
  X c= Y implies sup X c= sup Y
proof
  assume X c= Y;
  then
A1: On X c= On Y by Th9;
  On Y c= sup Y by Def3;
  then On X c= sup Y by A1;
  hence thesis by Def3;
end;
