reserve i,k for Nat;
reserve A for QC-alphabet;
reserve x for bound_QC-variable of A;
reserve a for free_QC-variable of A;
reserve p,q for Element of QC-WFF(A);
reserve l for FinSequence of QC-variables(A);
reserve P,Q for QC-pred_symbol of A;
reserve V for non empty Subset of QC-variables(A);
reserve s,t for QC-symbol of A;

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;
