reserve Al for QC-alphabet;
reserve a,b,c,d for object,
  i,j,k,m,n for Nat,
  p,q,r for Element of CQC-WFF(Al),
  x,y,y0 for bound_QC-variable of Al,
  X for Subset of CQC-WFF(Al),
  A for non empty set,
  J for interpretation of Al,A,
  v,w for Element of Valuations_in(Al,A),
  Sub for CQC_Substitution of Al,
  f,f1,g,h,h1 for FinSequence of CQC-WFF(Al);
reserve fin,fin1 for FinSequence;
reserve PR,PR1 for FinSequence of [:set_of_CQC-WFF-seq(Al),Proof_Step_Kinds:];
reserve a for Element of A;

theorem Th64:
  ex x st not x in still_not-bound_in f
proof
  still_not-bound_in f is finite by Th62;
  then still_not-bound_in f <> bound_QC-variables(Al) by Th63;
  then
  not ( for b being object holds b in still_not-bound_in f iff
   b in bound_QC-variables(Al)) by TARSKI:2;
  then consider b such that
A1: not b in still_not-bound_in f and
A2: b in bound_QC-variables(Al);
  reconsider x = b as bound_QC-variable of Al by A2;
  take x;
  thus thesis by A1;
end;
