reserve x,y,z,X,Y for set;
reserve X,Y for non empty set,
  f for Function of X,Y;

theorem Th9:
  for B being Element of Fin X st B <> {} ex x being Element of X st x in B
proof
  let B be Element of Fin X;
  set x = the Element of B;
  assume
A1: B <> {};
  then reconsider x as Element of X by Th6;
  take x;
  thus thesis by A1;
end;
