reserve A for QC-alphabet;
reserve a,b,b1,b2,c,d for object,
  i,j,k,n for Nat,
  x,y,x1,x2 for bound_QC-variable of A,
  P for QC-pred_symbol of k,A,
  ll for CQC-variable_list of k,A,
  l1 ,l2 for FinSequence of QC-variables(A),
  p for QC-formula of A,
  s,t for QC-symbol of A;
reserve Sub for CQC_Substitution of A;
reserve finSub for finite CQC_Substitution of A;
reserve e for Element of vSUB(A);
reserve S,S9,S1,S2,S19,S29,T1,T2 for Element of QC-Sub-WFF(A);
reserve B for Element of [:QC-Sub-WFF(A),bound_QC-variables(A):];
reserve SQ for second_Q_comp of B;

theorem Th27:
  not (ex S st S is Sub_atomic Sub_negative or S is Sub_atomic
  Sub_conjunctive or S is Sub_atomic Sub_universal or S is Sub_negative
  Sub_conjunctive or S is Sub_negative Sub_universal or S is Sub_conjunctive
Sub_universal or S is A-Sub_VERUM Sub_atomic or S is A-Sub_VERUM
Sub_negative or S
  is A-Sub_VERUM Sub_conjunctive or S is A-Sub_VERUM Sub_universal )
proof
  let S;
A1: S is Sub_negative implies ((@S`1).1)`1 = 1 by Th25;
A2: S is Sub_conjunctive implies ((@S`1).1)`1 = 2 by Th25;
A3: S is Sub_universal implies ((@S`1).1)`1 = 3 by Th25;
  S is A-Sub_VERUM implies ((@S`1).1)`1 = 0;
  hence thesis by A1,A2,A3,Th26;
end;
