reserve E,X,Y,x for set;
reserve A,B,C for Subset of E;

theorem
  for A,B st for x being Element of E holds not x in A iff x in B holds A = B`
proof
  let A,B;
  assume for x being Element of E holds not x in A iff x in B;
  then for x being Element of E holds x in A iff not x in B;
  hence thesis by Th30;
end;
