reserve fi,psi for Ordinal-Sequence,
  A,A1,B,C,D for Ordinal,
  X,Y for set,
  x,y for object;

theorem
  sup X c= succ union On X
proof
  reconsider A = union On X as Ordinal by Th5;
  On X c= succ A
  proof
    let x be object;
    assume
A1: x in On X;
    then reconsider a = x as Ordinal by ORDINAL1:def 9;
    a c= A by A1,ZFMISC_1:74;
    hence thesis by ORDINAL1:22;
  end;
  hence thesis by ORDINAL2:def 3;
end;
