theorem
  for SK1, SK2 be strict Subfield of K holds
  (SK1 = SK2 iff for x holds x in SK1 iff x in SK2)
  proof
    let SK1,SK2 be strict Subfield of K;
    thus SK1 = SK2 implies for x holds x in SK1 iff x in SK2;
    assume for x holds x in SK1 iff x in SK2;
    then SK1 is strict Subfield of SK2
    & SK2 is strict Subfield of SK1 by Th7;
    hence thesis by Th4;
  end;
