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 Th19:
  A in X implies A in sup X
proof
  assume A in X;
  then
A1: A in On X by ORDINAL1:def 9;
  On X c= sup X by Def3;
  hence thesis by A1;
end;
