Consider the following premises. For all x_8, if x_8 plays squash, then x_8 is a doctor. Linda is playing squash. For all x_8, if x_8 were a doctor, then x_8 is playing squash. Can we infer the following from them? If we can, name the inference rule being used: Linda is a doctor.
 From the fact that for all x_8, if x_8 plays squash, then x_8 is a doctor, and that for all x_8, if x_8 were a doctor, then x_8 is playing squash we can infer that for all x_8, x_8 will play squash if and only if x_8 is a doctor via universal biconditional introduction. From the fact that for all x_8, x_8 will play squash if and only if x_8 is a doctor we can infer that Linda is playing squash if and only if Linda is a doctor via universal instantiation. From the fact that Linda is playing squash if and only if Linda is a doctor we can infer that if Linda plays squash, then Linda is a doctor via biconditional elimination. Finally, from the fact that if Linda plays squash, then Linda is a doctor, and that Linda is playing squash we can infer that Linda is a doctor via modus ponens. Therefore, the answer is yes.