theorem Th97:
  |-_IPC ((p 'or' q) => FALSUM) =>((p => FALSUM) '&' (q => FALSUM))
proof
A1: (((p 'or' q) => FALSUM) => (p => FALSUM)) => ((((p 'or' q) => FALSUM)
    => (q => FALSUM)) =>
    (((p 'or' q) => FALSUM) => ((p => FALSUM) '&' (q => FALSUM))))
    in IPC-Taut by INTPRO_1:38;
A2: (p => (p 'or' q)) => (((p 'or' q) => FALSUM) => (p => FALSUM))
    in IPC-Taut by INTPRO_1:24;
  p => (p 'or' q) in IPC-Taut by INTPRO_1:def 14;
  then A3: ((p 'or' q) => FALSUM) => (p => FALSUM) in IPC-Taut
    by A2,INTPRO_1:def 14;
A4: (q => (p 'or' q)) => (((p 'or' q) => FALSUM) => (q => FALSUM))
    in IPC-Taut by INTPRO_1:24;
  q => (p 'or' q) in IPC-Taut by INTPRO_1:def 14;
  then A5: ((p 'or' q) => FALSUM) => (q => FALSUM) in IPC-Taut
    by A4,INTPRO_1:def 14;
  (((p 'or' q) => FALSUM) => (q => FALSUM)) =>
  (((p 'or' q) => FALSUM) => ((p => FALSUM) '&' (q => FALSUM)))
  in IPC-Taut by A1,A3,INTPRO_1:def 14;
  then ((p 'or' q) => FALSUM) =>((p => FALSUM) '&' (q => FALSUM))
  in IPC-Taut  by A5,INTPRO_1:def 14;
  hence thesis by Th69;
end;
