Consider the following premises. For all x_5, x_5 is a writer. For all x_5, if x_5 were a writer, then x_5 is writing a letter. For all x_5, if x_5 were a cashier, then x_5 is bored. For all x_5, if x_5 writes a letter, then x_5 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is bored.
 From the fact that for all x_5, if x_5 were a writer, then x_5 is writing a letter, and that for all x_5, x_5 is a writer we can infer that for all x_5, x_5 will write a letter via universal modus ponens. From the fact that for all x_5, if x_5 writes a letter, then x_5 is a cashier, and that for all x_5, x_5 will write a letter we can infer that for all x_5, x_5 is a cashier via universal modus ponens. Finally, from the fact that for all x_5, if x_5 were a cashier, then x_5 is bored, and that for all x_5, x_5 is a cashier we can infer that for all x_5, x_5 is bored via universal modus ponens. Therefore, the answer is yes.