1. (A→(B→C))→((A→B)→(A→C))    (axiom 2)

2. (A→(B→A))→((A→B)→(A→A))    (let C = A in formula 1)

3. A→(B→A)                    (axiom 1)

4. (A→B)→(A→A)                (modus ponens deduction from steps 2 and 3)

5. (A→(B→A))→(A→A)            (let B = B→A in step 4)

6. A→A                        (modus ponens deduction from steps 5 and 3)