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
  for p being QC-formula of A st p is closed holds All(x,p) is closed
proof
  let p be QC-formula of A;
  assume still_not-bound_in p = {};
  then still_not-bound_in p c= {x} by XBOOLE_1:2;
  hence thesis by Th23;
end;
