 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 Th75:
  |-_IPC ((p => q) '&' (p => (q => FALSUM))) => (p => FALSUM)
proof
  set Q = (p => q) '&' (p => (q => FALSUM));
   p in {p,Q} by TARSKI:def 2; then
A1: {p,Q} |-_IPC p by Th67;
    Q in {p,Q} by TARSKI:def 2; then
A2: {p,Q} |-_IPC Q by Th67;
    {p,Q} |-_IPC Q => (p => q) by Th20; then
    {p,Q} |-_IPC p => q by A2,Th27; then
A5: {p,Q} |-_IPC q by A1,Th27;
    {p,Q} |-_IPC Q => (p => (q => FALSUM)) by Th21; then
  {p,Q}|-_IPC p => (q => FALSUM) by A2,Th27; then
   {p,Q}|-_IPC q => FALSUM by A1,Th27; then
   {p,Q} |-_IPC FALSUM by A5,Th27; then
  {Q}|-_IPC p => FALSUM by Th55;
  hence thesis by Th54;
end;
