reserve T, X, Y for Subset of HP-WFF;
reserve p, q, r, s for Element of HP-WFF;

theorem Th23:
  p => q in HP_TAUT & q => r in HP_TAUT implies p => r in HP_TAUT
proof
  assume that
A1: p => q in HP_TAUT and
A2: q => r in HP_TAUT;
  (p => q) => ((q => r) => (p => r)) in HP_TAUT by Th21;
  then (q => r) => (p => r) in HP_TAUT by A1,Def10;
  hence thesis by A2,Def10;
end;
