Consider the following premises. There is at least one x_4 for which if x_4 were a scientist, then x_4 is writing a letter. For all x_4, if x_4 writes a letter, then x_4 is playing squash. For all x_4, if x_4 plays squash, then x_4 is a scientist. Can we infer the following from them? There is at least one x_4 for which if x_4 writes a letter, then x_4 is playing squash.
 From the fact that for all x_4, if x_4 plays squash, then x_4 is a scientist, and that there is at least one x_4 for which if x_4 were a scientist, then x_4 is writing a letter we can infer that there is at least one x_4 for which if x_4 plays squash, then x_4 is writing a letter. From the fact that for all x_4, if x_4 writes a letter, then x_4 is playing squash, and that there is at least one x_4 for which if x_4 plays squash, then x_4 is writing a letter we can infer that there is at least one x_4 for which x_4 will write a letter if and only if x_4 will play squash. Finally, from the fact that there is at least one x_4 for which x_4 will write a letter if and only if x_4 will play squash we can infer that there is at least one x_4 for which if x_4 writes a letter, then x_4 is playing squash. Therefore, the answer is yes.