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

theorem Th20:
  p => (q => r) in HP_TAUT implies q => (p => r) in HP_TAUT
proof
  assume
A1: p => (q => r) in HP_TAUT;
A2: ((p => q) => (p => r)) => ((q => (p => q)) => (q => (p => r))) in
  HP_TAUT by Th19;
  (p => (q => r)) => ((p => q) => (p => r)) in HP_TAUT by Def10;
  then ((p => q) => (p => r)) in HP_TAUT by A1,Def10;
  then
A3: ((q => (p => q)) => (q => (p => r))) in HP_TAUT by A2,Def10;
  q => (p => q) in HP_TAUT by Def10;
  hence thesis by A3,Def10;
end;
