theorem Th47:
  for p holds still_not-bound_in p c= Bound_Vars(p)
proof
  defpred P[Element of QC-WFF(Al)] means still_not-bound_in
   $1 c= Bound_Vars($1);
  Bound_Vars(VERUM(Al)) = {} by SUBSTUT1:2;
  then
A1: for p,q,x,k for l being CQC-variable_list of k,Al for P being
  QC-pred_symbol of k,Al holds P[VERUM(Al)] & P[P!l] &
  (P[p] implies P['not' p]) & (P[p] & P[q] implies P[p '&' q]) &
  (P[p] implies P[All(x,p)]) by Th43,Th44,Th45,Th46,QC_LANG3:3;
  thus for p holds P[p] from CQC_LANG:sch 1(A1);
end;
