Consider the following premises. Thomas is running if and only if Barbara is a doctor. For all z_3, if z_3 were excited, then z_3 is running. Barbara is not a doctor. Can we infer the following from them? Thomas is not excited.
 From the fact that for all z_3, if z_3 were excited, then z_3 is running we can infer that if Thomas were excited, then Thomas is running. From the fact that Thomas is running if and only if Barbara is a doctor, and that Barbara is not a doctor we can infer that Thomas is not running. Finally, from the fact that if Thomas were excited, then Thomas is running, and that Thomas is not running we can infer that Thomas is not excited. Therefore, the answer is yes.