Consider the following premises. For all x_11, x_11 is excited if and only if x_11 is poor. For all x_11, x_11 will climb a mountain or x_11 will work. For all x_11, x_11 is not excited. There is at least one x_11 for which x_11 will climb a mountain if and only if x_11 is poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 will work.
 From the fact that for all x_11, x_11 is excited if and only if x_11 is poor, and that for all x_11, x_11 is not excited we can infer that for all x_11, x_11 is not poor via universal biconditional elimination. From the fact that there is at least one x_11 for which x_11 will climb a mountain if and only if x_11 is poor, and that for all x_11, x_11 is not poor we can infer that there is at least one x_11 for which x_11 will not climb a mountain via existential biconditional elimination. Finally, from the fact that for all x_11, x_11 will climb a mountain or x_11 will work, and that there is at least one x_11 for which x_11 will not climb a mountain we can infer that there is at least one x_11 for which x_11 will work via existential disjunctive syllogism. Therefore, the answer is yes.