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 Th10:
  s.x in CQC-WFF(Al) & s.y in CQC-WFF(Al) & not x in still_not-bound_in s &
  s.x in Cn(X) implies s.y in Cn(X)
proof
  assume that
A1: s.x in CQC-WFF(Al) and
A2: s.y in CQC-WFF(Al) and
A3: not x in still_not-bound_in s and
A4: s.x in Cn(X);
  reconsider s1 = s.x as Element of CQC-WFF(Al) by A1;
  reconsider q = s.y as Element of CQC-WFF(Al) by A2;
 T is being_a_theory & X c= T implies q in T
  proof
    assume that
A5: T is being_a_theory and
A6: X c= T;
 s1 in T by A4,A5,A6,Def2;
    hence thesis by A3,A5;
  end;
  hence thesis by Def2;
end;
