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 Th9:
  X c= Y implies On X c= On Y
proof
  assume
A1: X c= Y;
  let x be object;
  assume x in On X;
  then x in X & x is Ordinal by ORDINAL1:def 9;
  hence thesis by A1,ORDINAL1:def 9;
end;
