theorem :: Modus Ponens for valid_IPC
  p is valid_IPC & p => q is valid_IPC implies q is valid_IPC
proof
A1: IPC-Taut is IPC_theory;
  assume p is valid_IPC & p => q is valid_IPC;
  then p in IPC-Taut & p => q in IPC-Taut;
  hence thesis by A1;
end;
