theorem Th9:
  p is conjunctive or p is conditional or p is simple or p = VERUM
proof
  defpred P[Element of HP-WFF] means $1 is conjunctive or $1 is conditional or
  $1 is simple or $1 = VERUM;
A1: P[VERUM];
A2: for n holds P[prop n] by Def8;
A3: for r,s st P[r] & P[s] holds P[r '&' s] & P[r => s] by Def6,Def7;
  for p holds P[p] from HPInd(A1,A2,A3);
  hence thesis;
end;
