[A]1   [A → B]4
              ---------------- 
        [¬B]2      B
        ------------------- 
                ⊥ 
             --------- (1)
    [¬¬A]3      ¬A
   ---------------- 
           ⊥ 
        ------- (2)
          ¬¬B
      ----------- (3)
       ¬¬A → ¬¬B
  --------------------- (4)
  (A → B) → (¬¬A → ¬¬B)