Consider the following premises. For all x_17, x_17 will work or x_17 will climb a mountain. For all x_17, if x_17 works, then x_17 is playing squash. For all x_17, if x_17 were a scientist, then x_17 is writing a letter. For all x_17, if x_17 were a janitor, then x_17 is writing a letter. There is at least one x_17 for which x_17 is a janitor or x_17 is a scientist. For all x_17, x_17 will climb a mountain if and only if x_17 will play squash. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_17 for which x_17 will write a letter and x_17 will play squash.
 From the fact that for all x_17, if x_17 were a janitor, then x_17 is writing a letter, that for all x_17, if x_17 were a scientist, then x_17 is writing a letter, and that there is at least one x_17 for which x_17 is a janitor or x_17 is a scientist we can infer that there is at least one x_17 for which x_17 will write a letter via existential disjunction elimination. From the fact that for all x_17, x_17 will climb a mountain if and only if x_17 will play squash we can infer that for all x_17, if x_17 climbs a mountain, then x_17 is playing squash via universal biconditional elimination. From the fact that for all x_17, if x_17 works, then x_17 is playing squash, that for all x_17, if x_17 climbs a mountain, then x_17 is playing squash, and that for all x_17, x_17 will work or x_17 will climb a mountain we can infer that for all x_17, x_17 will play squash via universal disjunction elimination. Finally, from the fact that there is at least one x_17 for which x_17 will write a letter, and that for all x_17, x_17 will play squash we can infer that there is at least one x_17 for which x_17 will write a letter and x_17 will play squash via existential conjunction. Therefore, the answer is yes.