reserve A for QC-alphabet;
reserve i,j,k,l,m,n for Nat;
reserve a,b,e for set;
reserve t,u,v,w,z for QC-symbol of A;
reserve p,q,r,s for Element of CQC-WFF(A);
reserve x for Element of bound_QC-variables(A);
reserve ll for CQC-variable_list of k,A;
reserve P for QC-pred_symbol of k,A;

theorem Th12:
  p is_subformula_of All(x,p)
proof
  p is_proper_subformula_of All(x,p) by QC_LANG2:71;
  hence thesis by QC_LANG2:def 21;
end;
