theorem
  A^Fodelta = A^Fob \ A^Foi
proof
  for x being object holds x in A^Fodelta iff x in A^Fob \ A^Foi
  proof
    let x be object;
    thus x in A^Fodelta implies x in A^Fob \ A^Foi
    proof
      assume x in A^Fodelta;
      then x in (A^Fob) /\ (((A`)^Fob)`)` by Th39;
      then x in ((A^Fob) /\ (A^Foi)`) by Th37;
      hence thesis by SUBSET_1:13;
    end;
    assume x in A^Fob \ A^Foi;
    then x in ((A^Fob) /\ ((A^Foi)`)) by SUBSET_1:13;
    then x in ((A^Fob) /\ (((A`)^Fob)`)`) by Th37;
    hence thesis by Th39;
  end;
  hence thesis by TARSKI:2;
end;
