Consider the following premises. For all x_6, if x_6 takes a plane, then x_6 is a writer. For all x_6, if x_6 were a writer, then x_6 is playing tennis. There is at least one x_6 for which if x_6 were a writer, then x_6 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which if x_6 takes a plane, then x_6 is playing tennis.
 From the fact that there is at least one x_6 for which if x_6 were a writer, then x_6 is taking a plane, and that for all x_6, if x_6 takes a plane, then x_6 is a writer we can infer that there is at least one x_6 for which x_6 is a writer if and only if x_6 will take a plane via existential biconditional introduction. From the fact that there is at least one x_6 for which x_6 is a writer if and only if x_6 will take a plane we can infer that there is at least one x_6 for which if x_6 takes a plane, then x_6 is a writer via existential biconditional elimination. Finally, from the fact that there is at least one x_6 for which if x_6 takes a plane, then x_6 is a writer, and that for all x_6, if x_6 were a writer, then x_6 is playing tennis we can infer that there is at least one x_6 for which if x_6 takes a plane, then x_6 is playing tennis via existential transitivity. Therefore, the answer is yes.