Consider the following premises. For all x_5, x_5 is a nurse. For all x_5, if x_5 were a nurse, then x_5 is poor. For all x_5, x_5 is sad if and only if x_5 is poor. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is poor.
 From the fact that for all x_5, x_5 is sad if and only if x_5 is poor we can infer that for all x_5, if x_5 were sad, then x_5 is poor via universal biconditional elimination. From the fact that for all x_5, x_5 is a nurse we can infer that for all x_5, x_5 is a nurse or x_5 is sad via universal addition. Finally, from the fact that for all x_5, if x_5 were a nurse, then x_5 is poor, that for all x_5, if x_5 were sad, then x_5 is poor, and that for all x_5, x_5 is a nurse or x_5 is sad we can infer that for all x_5, x_5 is poor via universal disjunction elimination. Therefore, the answer is yes.