Consider the following premises. There is at least one x_3 for which if x_3 were a writer, then x_3 is sad. For all x_3, if x_3 were bored, then x_3 is a writer. For all x_3, if x_3 were sad, then x_3 is bored. For all x_3, x_3 is not sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which x_3 is not a writer.
 From the fact that for all x_3, if x_3 were sad, then x_3 is bored, and that for all x_3, if x_3 were bored, then x_3 is a writer we can infer that for all x_3, if x_3 were sad, then x_3 is a writer via universal transitivity. From the fact that there is at least one x_3 for which if x_3 were a writer, then x_3 is sad, and that for all x_3, if x_3 were sad, then x_3 is a writer we can infer that there is at least one x_3 for which x_3 is a writer if and only if x_3 is sad via existential biconditional introduction. Finally, from the fact that there is at least one x_3 for which x_3 is a writer if and only if x_3 is sad, and that for all x_3, x_3 is not sad we can infer that there is at least one x_3 for which x_3 is not a writer via existential biconditional elimination. Therefore, the answer is yes.