Consider the following premises. For all x_3, if x_3 were a taxi driver, then x_3 is playing squash. For all x_3, if x_3 takes a plane, then x_3 is a taxi driver. There is at least one x_3 for which if x_3 plays squash, then x_3 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_3 for which if x_3 were a taxi driver, then x_3 is playing squash.
 From the fact that there is at least one x_3 for which if x_3 plays squash, then x_3 is taking a plane, and that for all x_3, if x_3 takes a plane, then x_3 is a taxi driver we can infer that there is at least one x_3 for which if x_3 plays squash, then x_3 is a taxi driver via existential transitivity. From the fact that there is at least one x_3 for which if x_3 plays squash, then x_3 is a taxi driver, and that for all x_3, if x_3 were a taxi driver, then x_3 is playing squash we can infer that there is at least one x_3 for which x_3 will play squash if and only if x_3 is a taxi driver via existential biconditional introduction. Finally, from the fact that there is at least one x_3 for which x_3 will play squash if and only if x_3 is a taxi driver we can infer that there is at least one x_3 for which if x_3 were a taxi driver, then x_3 is playing squash via existential biconditional elimination. Therefore, the answer is yes.