theorem Th90:
  |-_IPC ((p '&' q) => FALSUM) => (q => (p => FALSUM))
proof
  set U = (p '&' q) => FALSUM;
  set X = {p,q,U};
A0: q in X & p in X & U in X by ENUMSET1:def 1; then
A1: X |-_IPC U by Th67;
A2: X |-_IPC p by A0,Th67;
A3: X |-_IPC q by A0,Th67;
    X |-_IPC p => (q => (p '&' q)) by Th22; then
   X |-_IPC q => (p '&' q) by A2,Th27; then
    X |-_IPC p '&' q by A3,Th27; then
  {p,q,U} |-_IPC FALSUM by A1,Th27; then
  {q,U} |-_IPC p => FALSUM by Th56; then
  {U} |-_IPC q => (p => FALSUM) by Th55;
  hence thesis by Th54;
end;
