 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 Th97:
  |-_IPC ((p 'or' q) => FALSUM) =>((p => FALSUM) '&' (q => FALSUM))
proof
A1: (((p 'or' q) => FALSUM) => (p => FALSUM)) => ((((p 'or' q) => FALSUM)
    => (q => FALSUM)) =>
    (((p 'or' q) => FALSUM) => ((p => FALSUM) '&' (q => FALSUM))))
    in IPC-Taut by INTPRO_1:38;
A2: (p => (p 'or' q)) => (((p 'or' q) => FALSUM) => (p => FALSUM))
    in IPC-Taut by INTPRO_1:24;
  p => (p 'or' q) in IPC-Taut by INTPRO_1:def 14;
  then A3: ((p 'or' q) => FALSUM) => (p => FALSUM) in IPC-Taut
    by A2,INTPRO_1:def 14;
A4: (q => (p 'or' q)) => (((p 'or' q) => FALSUM) => (q => FALSUM))
    in IPC-Taut by INTPRO_1:24;
  q => (p 'or' q) in IPC-Taut by INTPRO_1:def 14;
  then A5: ((p 'or' q) => FALSUM) => (q => FALSUM) in IPC-Taut
    by A4,INTPRO_1:def 14;
  (((p 'or' q) => FALSUM) => (q => FALSUM)) =>
  (((p 'or' q) => FALSUM) => ((p => FALSUM) '&' (q => FALSUM)))
  in IPC-Taut by A1,A3,INTPRO_1:def 14;
  then ((p 'or' q) => FALSUM) =>((p => FALSUM) '&' (q => FALSUM))
  in IPC-Taut  by A5,INTPRO_1:def 14;
  hence thesis by Th69;
end;
