theorem Th17:
  for p being QC-formula of A st p is biconditional holds
  still_not-bound_in p = (still_not-bound_in the_left_side_of p) \/ (
  still_not-bound_in the_right_side_of p)
proof
  let p be QC-formula of A;
  set p1 = the_left_side_of p;
  set p2 = the_right_side_of p;
  assume p is biconditional;
  then p = (the_left_side_of p) <=> (the_right_side_of p) by QC_LANG2:39;
  then p = (p1 => p2) '&' (p2 => p1) by QC_LANG2:def 4;
  then still_not-bound_in p = (still_not-bound_in p1 => p2) \/ (
  still_not-bound_in p2 => p1) by Th10
    .= (still_not-bound_in p1) \/ (still_not-bound_in p2) \/ (
  still_not-bound_in p2 => p1) by Th16
    .= (still_not-bound_in p1) \/ (still_not-bound_in p2) \/ ((
  still_not-bound_in p1) \/ (still_not-bound_in p2)) by Th16
    .= (still_not-bound_in p1) \/ (still_not-bound_in p2);
  hence thesis;
end;
