 reserve i,j,n,k,l for Nat;
 reserve T,S,X,Y,Z for Subset of MC-wff;
 reserve p,q,r,t,F,H,G for Element of MC-wff;
 reserve s,U,V for MC-formula;
reserve f,g for FinSequence of [:MC-wff,Proof_Step_Kinds_IPC:];
 reserve X,T for Subset of MC-wff;
 reserve F,G,H,p,q,r,t for Element of MC-wff;
 reserve s,h for MC-formula;
 reserve f for FinSequence of [:MC-wff,Proof_Step_Kinds_IPC:];
 reserve i,j for Element of NAT;
 reserve F1,F2,F3,F4,F5,F6,F7,F8,F9,F10,G for MC-formula;
 reserve x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x for Element of MC-wff;
reserve x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 for object;

theorem Th88:
  |-_IPC (p => (q => FALSUM)) => ((p '&' q) => FALSUM)
proof
  set U = p => (q => FALSUM);
  set X = {p '&' q,U};
A0: p '&' q in X & U in X by TARSKI:def 2; then
A1: X |-_IPC U by Th67;
A2: X |-_IPC p '&' q by A0,Th67;
    X |-_IPC (p '&' q) => p by Th20; then
A4: X |-_IPC p by A2,Th27;
    X |-_IPC (p '&' q) => q by Th21; then
A6: X |-_IPC q by A2,Th27;
   X |-_IPC q => FALSUM by A1,A4,Th27; then
   X |-_IPC FALSUM by A6,Th27; then
  {U} |-_IPC (p '&' q) => FALSUM by Th55;
  hence thesis by Th54;
end;
