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 c being Element of fixed_QC-variables(A) for a being Element of
  free_QC-variables(A) holds c <> a
proof
  let c be Element of fixed_QC-variables(A);
  let a be Element of free_QC-variables(A);
  consider a1,a2 being object such that
A1: a1 in {6} and
  a2 in NAT and
A2: a = [a1,a2] by ZFMISC_1:def 2;
  consider c1,c2 being object such that
A3: c1 in {5} and
  c2 in QC-symbols(A) and
A4: c = [c1,c2] by ZFMISC_1:def 2;
A5: c1 = 5 by A3,TARSKI:def 1;
  a1 = 6 by A1,TARSKI:def 1;
  hence thesis by A2,A4,A5,XTUPLE_0:1;
end;
