 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 Th128:
  |-_IPC (p => q) => (((q 'or' r)=> FALSUM) => ((p 'or' r)=> FALSUM))
proof
    p 'or' r in {p 'or' r,(q 'or' r)=> FALSUM,p => q} by ENUMSET1:def 1; then
A1: {p 'or' r,(q 'or' r)=> FALSUM,p => q} |-_IPC p 'or' r by Th67;
   (q 'or' r)=> FALSUM in {p 'or' r,(q 'or' r)=> FALSUM,p => q}
       by ENUMSET1:def 1; then
A2: {p 'or' r,(q 'or' r)=> FALSUM,p => q} |-_IPC (q 'or' r)=> FALSUM
      by Th67;
    p => q in {p 'or' r,(q 'or' r)=> FALSUM,p => q} by ENUMSET1:def 1; then
A3: {p 'or' r,(q 'or' r)=> FALSUM,p => q} |-_IPC p => q by Th67;
A04: |-_IPC (p => q) => ((p 'or' r) => (q 'or' r)) by Th69,INTPRO_1:60;
   {}(MC-wff) c= {p 'or' r,(q 'or' r)=> FALSUM,p => q}; then
    {p 'or' r,(q 'or' r)=> FALSUM,p => q}
     |-_IPC (p => q) => ((p 'or' r) => (q 'or' r)) by A04,Th66; then
   {p 'or' r,(q 'or' r)=> FALSUM,p => q} |-_IPC (p 'or' r) => (q 'or' r)
       by A3,Th27; then
    {p 'or' r,(q 'or' r)=> FALSUM,p => q} |-_IPC q 'or' r
      by A1,Th27; then
    {p 'or' r,(q 'or' r)=> FALSUM,p => q} |-_IPC FALSUM by A2,Th27; then
    {(q 'or' r)=> FALSUM,p => q} |-_IPC (p 'or' r)=> FALSUM
      by Th56; then
    {p => q} |-_IPC ((q 'or' r)=> FALSUM) => ((p 'or' r)=> FALSUM) by Th55;
    hence thesis by Th54;
end;
