 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 Th107:
  |-_IPC (p '&' (q => FALSUM)) => ((p => q) => FALSUM)
proof
   p => q in {p => q,p '&' (q => FALSUM)} by TARSKI:def 2; then
A1: {p => q,p '&' (q => FALSUM)} |-_IPC p => q by Th67;
   p '&' (q => FALSUM) in {p => q,p '&' (q => FALSUM)} by TARSKI:def 2; then
A2: {p => q,p '&' (q => FALSUM)} |-_IPC p '&' (q => FALSUM) by Th67;
    {p => q,p '&' (q => FALSUM)} |-_IPC (p '&' (q => FALSUM)) => p by Th20;
     then
   {p => q,p '&' (q => FALSUM)} |-_IPC p by A2,Th27; then
A4: {p => q,p '&' (q => FALSUM)} |-_IPC q by A1,Th27;
   {p => q,p '&' (q => FALSUM)} |-_IPC (p '&' (q => FALSUM)) =>
     (q => FALSUM) by Th21; then
  {p => q,p '&' (q => FALSUM)} |-_IPC q => FALSUM by A2,Th27; then
  {p '&' (q => FALSUM),p => q} |-_IPC FALSUM by A4,Th27; then
  {p '&' (q => FALSUM)} |-_IPC  (p => q) => FALSUM by Th55;
  hence thesis by Th54;
end;
