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 Th15:
  for p being QC-formula of A st p is conditional holds
  still_not-bound_in p = (still_not-bound_in the_antecedent_of p) \/ (
  still_not-bound_in the_consequent_of p)
proof
  let p be QC-formula of A;
  set p1 = the_antecedent_of p;
  set p2 = the_consequent_of p;
  assume p is conditional;
  then p = (the_antecedent_of p) => (the_consequent_of p) by QC_LANG2:38;
  then p = 'not'(p1 '&' 'not' p2) by QC_LANG2:def 2;
  then still_not-bound_in p = still_not-bound_in p1 '&' 'not' p2 by Th7
    .= (still_not-bound_in p1) \/ (still_not-bound_in 'not' p2) by Th10
    .= (still_not-bound_in p1) \/ (still_not-bound_in p2) by Th7;
  hence thesis;
end;
