 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;

theorem Th49:
  X |-_IPC p => p
proof
A1: X |-_IPC p => (p => p) by INTPRO_1:1;
A2: X |-_IPC p => ((p => p) => p) by INTPRO_1:1;
  X |-_IPC (p => ((p => p) => p)) => ((p => (p => p)) => (p => p))
    by INTPRO_1:2;
  then X |-_IPC (p => (p => p)) => (p => p) by A2,Th27;
  hence thesis by A1,Th27;
end;
