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

theorem Th24:
  (p => (q => r)) => ((s => q) => (p => (s => r))) in HP_TAUT
proof
A1: (((q => r) => (s => r)) => (p => (s => r))) => ((s => q) => (p => (s =>
  r))) in HP_TAUT by Lm4;
  ((((q => r) => (s => r)) => (p => (s => r))) => ((s => q) => (p => (s =>
r)))) => ((p => (q => r)) => ((s => q) => (p => (s => r)))) in HP_TAUT by Lm4;
  hence thesis by A1,Def10;
end;
