reserve A for QC-alphabet;
reserve k,n,m for Nat;
reserve P for QC-pred_symbol of A;
reserve F for Element of QC-WFF(A);
reserve Q for QC-pred_symbol of A;
reserve F, G for (Element of QC-WFF(A)), s for FinSequence;
reserve p for Element of QC-WFF(A);
reserve F for Element of QC-WFF(A);
reserve p for Element of QC-WFF(A);

theorem Th20:
  not (VERUM(A) is atomic or VERUM(A) is negative or VERUM(A) is
  conjunctive or VERUM(A) is universal)
  & not (ex p st p is atomic & p is negative
  or p is atomic & p is conjunctive or p is atomic & p is universal or p is
  negative & p is conjunctive or p is negative & p is universal or p is
  conjunctive & p is universal)
proof
  (@VERUM(A).1)`1 = 0;
  hence not (VERUM(A) is atomic or VERUM(A)
  is negative or VERUM(A) is conjunctive or
  VERUM(A) is universal) by Th18,Th19;
  let p be Element of QC-WFF(A);
A1: p is conjunctive implies (@p.1)`1 = 2 by Th18;
A2: p is universal implies (@p.1)`1 = 3 by Th18;
  p is negative implies (@p.1)`1 = 1 by Th18;
  hence thesis by A1,A2,Th19;
end;
