Consider the following premises. For all x_17, x_17 will write a letter and x_17 will play squash. For all z_3, z_3 will work. For all z_3, if z_3 works, then z_3 is making tea. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_3 for which z_3 will write a letter and z_3 will make tea.
 From the fact that for all x_17, x_17 will write a letter and x_17 will play squash we can infer that for all x_17, x_17 will write a letter via universal simplification. From the fact that for all z_3, if z_3 works, then z_3 is making tea, and that for all z_3, z_3 will work we can infer that for all z_3, z_3 will make tea via universal modus ponens. From the fact that for all x_17, x_17 will write a letter we can infer that Jennifer is writing a letter via universal instantiation. From the fact that Jennifer is writing a letter we can infer that there is at least one z_3 for which z_3 will write a letter via existential generalization. Finally, from the fact that there is at least one z_3 for which z_3 will write a letter, and that for all z_3, z_3 will make tea we can infer that there is at least one z_3 for which z_3 will write a letter and z_3 will make tea via existential conjunction. Therefore, the answer is yes.