 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:];

theorem Th40:
  (p => (q => r)) => ((p => q) => (p => r)) is valid_IPC
proof
  (p => (q => r)) => ((p => q) => (p => r)) in IPC-Taut
  proof
    IPC-Taut is IPC_theory;
    hence thesis;
  end;
  hence thesis;
end;
