reserve Al for QC-alphabet;
reserve i,j,n,k,l for Nat;
reserve a for set;
reserve T,S,X,Y for Subset of CQC-WFF(Al);
reserve p,q,r,t,F,H,G for Element of CQC-WFF(Al);
reserve s for QC-formula of Al;
reserve x,y for bound_QC-variable of Al;

theorem Th9:
  p => q in Cn(X) & not x in still_not-bound_in p implies
  p => All(x,q) in Cn(X)
proof
  assume that
A1: p => q in Cn(X) and
A2: not x in still_not-bound_in p;
 T is being_a_theory & X c= T implies p => All(x,q) in T
  proof
    assume that
A3: T is being_a_theory and
A4: X c= T;
 p => q in T by A1,A3,A4,Def2;
    hence thesis by A2,A3;
  end;
  hence thesis by Def2;
end;
