theorem Th94:
  |-_IPC q => (p => (((p '&' q) => FALSUM) => FALSUM))
proof
    (p '&' q) => FALSUM in {(p '&' q) => FALSUM,p,q} by ENUMSET1:def 1; then
A1: {(p '&' q) => FALSUM,p,q} |-_IPC (p '&' q) => FALSUM by Th67;
    p in {(p '&' q) => FALSUM,p,q} by ENUMSET1:def 1; then
A2: {(p '&' q) => FALSUM,p,q} |-_IPC p by Th67;
    q in {(p '&' q) => FALSUM,p,q} by ENUMSET1:def 1; then
A3: {(p '&' q) => FALSUM,p,q} |-_IPC q by Th67;
A04: |-_IPC p => (q => (p '&' q)) by Th22;
   {}(MC-wff) c= {(p '&' q) => FALSUM,p,q}; then
   {(p '&' q) => FALSUM,p,q} |-_IPC p => (q => (p '&' q))
       by A04,Th66; then
   {(p '&' q) => FALSUM,p,q} |-_IPC q => (p '&' q) by A2,Th27;
      then
   {(p '&' q) => FALSUM,p,q} |-_IPC p '&' q by A3,Th27; then
   {(p '&' q) => FALSUM,p,q} |-_IPC FALSUM by A1,Th27; then
  {p,q} |-_IPC ((p '&' q) => FALSUM) => FALSUM by Th56; then
  {q} |-_IPC p => (((p '&' q) => FALSUM) => FALSUM) by Th55;
  hence thesis by Th54;
end;
