reserve x for set;
reserve i,j for Integer;
reserve n,n1,n2,n3 for Nat;
reserve K,K1,K2,K3 for Field;
reserve SK1,SK2 for Subfield of K;
reserve ek,ek1,ek2 for Element of K;

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;
