Consider the following premises. If John climbs a mountain, then Jessica is a server. Jessica is a server if and only if Barbara is a nurse. Barbara is not a nurse. If Jessica were a server, then John is climbing a mountain. Can we infer the following from them? John is not climbing a mountain.
 From the fact that if John climbs a mountain, then Jessica is a server, and that if Jessica were a server, then John is climbing a mountain we can infer that John is climbing a mountain if and only if Jessica is a server. From the fact that Jessica is a server if and only if Barbara is a nurse, and that Barbara is not a nurse we can infer that Jessica is not a server. Finally, from the fact that John is climbing a mountain if and only if Jessica is a server, and that Jessica is not a server we can infer that John is not climbing a mountain. Therefore, the answer is yes.