theorem Th75:
  |-_IPC ((p => q) '&' (p => (q => FALSUM))) => (p => FALSUM)
proof
  set Q = (p => q) '&' (p => (q => FALSUM));
   p in {p,Q} by TARSKI:def 2; then
A1: {p,Q} |-_IPC p by Th67;
    Q in {p,Q} by TARSKI:def 2; then
A2: {p,Q} |-_IPC Q by Th67;
    {p,Q} |-_IPC Q => (p => q) by Th20; then
    {p,Q} |-_IPC p => q by A2,Th27; then
A5: {p,Q} |-_IPC q by A1,Th27;
    {p,Q} |-_IPC Q => (p => (q => FALSUM)) by Th21; then
  {p,Q}|-_IPC p => (q => FALSUM) by A2,Th27; then
   {p,Q}|-_IPC q => FALSUM by A1,Th27; then
   {p,Q} |-_IPC FALSUM by A5,Th27; then
  {Q}|-_IPC p => FALSUM by Th55;
  hence thesis by Th54;
end;
