1 (->I (if (and B C) (and (if A B) (if A C)))
     (proof
     2 (hyp (and B C))
     3 (->I (if A B)
          (proof
          4 (hyp A)
          5 (&E B 2)))
     6 (->I (if A C)
          (proof
          7 (hyp A)
          8 (&E C 2)))
     9 (&I (and (if A B) (if A C)) 3 6)))