reserve A for QC-alphabet;
reserve i,j,k for Nat;
reserve f for Substitution of A;

theorem Th4:
  for p being Element of QC-WFF(A) holds
  p is Element of CQC-WFF(A) iff Fixed p = {} & Free p = {}
proof
  let p be Element of QC-WFF(A);
  thus p is Element of CQC-WFF(A) implies Fixed p = {} & Free p = {}
  proof
    assume p is Element of CQC-WFF(A);
    then p in CQC-WFF(A);
    then ex s being QC-formula of A st s = p & Fixed s = {} & Free s = {};
    hence thesis;
  end;
  assume Fixed p = {} & Free p = {};
  then p in CQC-WFF(A);
  hence thesis;
end;
