Consider the following premises. For all x_9, x_9 is not a scientist. For all x_9, if x_9 plays tennis, then x_9 is a doctor. There is at least one x_9 for which if x_9 plays tennis, then x_9 is a scientist. For all x_9, if x_9 were a doctor, then x_9 is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is a doctor.
 From the fact that for all x_9, if x_9 were a doctor, then x_9 is playing tennis, and that for all x_9, if x_9 plays tennis, then x_9 is a doctor we can infer that for all x_9, x_9 is a doctor if and only if x_9 will play tennis via universal biconditional introduction. From the fact that there is at least one x_9 for which if x_9 plays tennis, then x_9 is a scientist, and that for all x_9, x_9 is not a scientist we can infer that there is at least one x_9 for which x_9 will not play tennis via existential modus tollens. Finally, from the fact that for all x_9, x_9 is a doctor if and only if x_9 will play tennis, and that there is at least one x_9 for which x_9 will not play tennis we can infer that there is at least one x_9 for which x_9 is not a doctor via existential biconditional elimination, which contradicts that For all x_9, x_9 is a doctor. Therefore, the answer is no.