Consider the following premises. For all x_10, if x_10 were a cashier, then x_10 is poor. For all x_10, if x_10 reads a book, then x_10 is writing a letter. There is at least one x_10 for which if x_10 cooks, then x_10 is reading a book. For all x_10, if x_10 writes a letter, then x_10 is making tea. For all x_10, if x_10 makes tea, then x_10 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which if x_10 cooks, then x_10 is poor.
 From the fact that for all x_10, if x_10 writes a letter, then x_10 is making tea, and that for all x_10, if x_10 makes tea, then x_10 is a cashier we can infer that for all x_10, if x_10 writes a letter, then x_10 is a cashier via universal transitivity. From the fact that for all x_10, if x_10 writes a letter, then x_10 is a cashier, and that for all x_10, if x_10 were a cashier, then x_10 is poor we can infer that for all x_10, if x_10 writes a letter, then x_10 is poor via universal transitivity. From the fact that there is at least one x_10 for which if x_10 cooks, then x_10 is reading a book, and that for all x_10, if x_10 reads a book, then x_10 is writing a letter we can infer that there is at least one x_10 for which if x_10 cooks, then x_10 is writing a letter via existential transitivity. Finally, from the fact that there is at least one x_10 for which if x_10 cooks, then x_10 is writing a letter, and that for all x_10, if x_10 writes a letter, then x_10 is poor we can infer that there is at least one x_10 for which if x_10 cooks, then x_10 is poor via existential transitivity. Therefore, the answer is yes.