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 Th16:
  for p,q being QC-formula of A holds still_not-bound_in p => q = (
  still_not-bound_in p) \/ (still_not-bound_in q)
proof
  let p,q be QC-formula of A;
A1: the_consequent_of(p => q) = q by QC_LANG2:30;
  p => q is conditional & the_antecedent_of(p => q) = p by QC_LANG2:30,def 11;
  hence thesis by A1,Th15;
end;
