Suppose A -> B. We will show that ~ B -> ~ A.
It is enough to assume A -> B, ~ B and show ~ A.
Thus, by rewriting ~ A we may assume A -> B, ~ B and show A -> _|_.
It is enough to assume A, A -> B, ~ B and show _|_.
Then, by Modus ponens, we get A, A -> B, B, ~ B to prove _|_.
In particular we get B, ~ B to prove _|_.
Hence we get _|_ as desired.