 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 Th114:
 |-_IPC (((p => q) => FALSUM)=> FALSUM) =>
          (p => ((q => FALSUM) => FALSUM))
proof
   p in {p,((p => q) => FALSUM)=> FALSUM} by TARSKI:def 2; then
A1: {p,((p => q) => FALSUM)=> FALSUM} |-_IPC p by Th67;
    ((p => q) => FALSUM)=> FALSUM in {p,((p => q) => FALSUM)=> FALSUM}
       by TARSKI:def 2; then
A2: {p,((p => q) => FALSUM)=> FALSUM} |-_IPC ((p => q) => FALSUM)=> FALSUM
      by Th67;
A03: |-_IPC (((p => q) => FALSUM) => FALSUM)
     => (((p => FALSUM) => FALSUM) => ((q => FALSUM) => FALSUM)) by Th108;
A04: {}(MC-wff) c= {p,((p => q) => FALSUM)=> FALSUM}; then
   {((p => q) => FALSUM)=> FALSUM,p} |-_IPC (((p => q) => FALSUM)=> FALSUM)
    => (((p => FALSUM) => FALSUM) => ((q => FALSUM) => FALSUM))
      by A03,Th66; then
A4: {p,((p => q) => FALSUM)=> FALSUM}
  |-_IPC ((p => FALSUM) => FALSUM) => ((q => FALSUM) => FALSUM) by A2,Th27;
   |-_IPC p => ((p => FALSUM) => FALSUM) by Th72; then
   {p,((p => q) => FALSUM)=> FALSUM} |-_IPC p => ((p => FALSUM) => FALSUM)
      by A04,Th66; then
   {p,((p => q) => FALSUM)=> FALSUM}|-_IPC ((p => FALSUM) => FALSUM)
     by A1,Th27; then
   {p,((p => q) => FALSUM)=> FALSUM}|-_IPC ((q => FALSUM) => FALSUM)
      by A4,Th27; then
  {((p => q) => FALSUM)=> FALSUM}|-_IPC p => ((q => FALSUM) => FALSUM)
      by Th55;
  hence thesis by Th54;
end;
