If you have givens of the forms *P*→*Q*
and ¬*Q*, then
you may infer ¬*P*. Select the givens
and give the Modus Tollens command, and Proof Designer will make the
inference.

You can also use this command to work backwards from your goal. If you
have a given of the form *P*→*Q*
and your goal is ¬*P*, then you could
complete the proof by first proving ¬*Q*
and then using modus tollens to infer ¬*P* from
*P*→*Q* and ¬*Q*.
If you want to do this, select the given *P*→*Q*
and the goal ¬*P* and give the Modus Tollens command.
Proof Designer will say that you now have to prove ¬*Q*,
and it will say that once ¬*Q* has been proven,
it can be used, together with *P*→*Q*, to infer
¬*P*.