Consider the following premises. If David climbs a mountain, then Charles is a mechanic. If Charles were a mechanic, then David is climbing a mountain. Charles is a mechanic if and only if it is raining. It is not raining. Can we infer the following from them? David is not climbing a mountain.
 From the fact that if Charles were a mechanic, then David is climbing a mountain, and that if David climbs a mountain, then Charles is a mechanic we can infer that Charles is a mechanic if and only if David is climbing a mountain. From the fact that Charles is a mechanic if and only if it is raining, and that it is not raining we can infer that Charles is not a mechanic. Finally, from the fact that Charles is a mechanic if and only if David is climbing a mountain, and that Charles is not a mechanic we can infer that David is not climbing a mountain. Therefore, the answer is yes.