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

theorem Th27: :: A Hilbert axiom
  (p => (p => q)) => (p => q) in HP_TAUT
proof
  (p => (p => q)) => ((p => p) => (p => q)) in HP_TAUT by Def10;
  then
A1: (p => p) => ((p => (p => q)) => (p => q)) in HP_TAUT by Th20;
  p => p in HP_TAUT by Th14;
  hence thesis by A1,Def10;
end;
