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

theorem Th19:
  (q => r) => ((p => q) => (p => r)) in HP_TAUT
proof
A1: ((p => (q => r)) => ((p => q) => (p => r))) in HP_TAUT by Def10;
A2: ( (q => r) => ((p => (q => r)) => ((p => q) => (p => r)))) => (((q => r)
  => (p => (q => r))) => ((q => r) => ((p => q) => (p => r)))) in HP_TAUT by
Def10;
  ((p => (q => r)) => ((p => q) => (p => r))) => ( (q => r) => ((p => (q
  => r)) => ((p => q) => (p => r)))) in HP_TAUT by Def10;
  then
  ( (q => r) => ((p => (q => r)) => ((p => q) => (p => r)))) in HP_TAUT by A1
,Def10;
  then
A3: ((q => r) => (p => (q => r))) => ((q => r) => ((p => q) => (p => r))) in
  HP_TAUT by A2,Def10;
  (q => r) => (p => (q => r)) in HP_TAUT by Def10;
  hence thesis by A3,Def10;
end;
