Consider the following premises. For all x_4, if x_4 drives a car, then x_4 is a politician. For all x_4, x_4 will play squash or x_4 will drive a car. There is at least one x_4 for which x_4 will play squash if and only if x_4 is a politician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 is a politician.
 From the fact that there is at least one x_4 for which x_4 will play squash if and only if x_4 is a politician we can infer that there is at least one x_4 for which if x_4 plays squash, then x_4 is a politician via existential biconditional elimination. Finally, from the fact that there is at least one x_4 for which if x_4 plays squash, then x_4 is a politician, that for all x_4, if x_4 drives a car, then x_4 is a politician, and that for all x_4, x_4 will play squash or x_4 will drive a car we can infer that there is at least one x_4 for which x_4 is a politician via existential disjunction elimination. Therefore, the answer is yes.