Consider the following premises. For all x_1, x_1 will write a letter if and only if x_1 will play squash. For all x_1, x_1 will play squash if and only if x_1 will write a letter. For all x_1, x_1 will not play squash. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, x_1 will not write a letter.
 From the fact that for all x_1, x_1 will write a letter if and only if x_1 will play squash we can infer that for all x_1, if x_1 plays squash, then x_1 is writing a letter via universal biconditional elimination. From the fact that for all x_1, x_1 will play squash if and only if x_1 will write a letter we can infer that for all x_1, if x_1 writes a letter, then x_1 is playing squash via universal biconditional elimination. From the fact that for all x_1, if x_1 writes a letter, then x_1 is playing squash, and that for all x_1, if x_1 plays squash, then x_1 is writing a letter we can infer that for all x_1, x_1 will write a letter if and only if x_1 will play squash via universal biconditional introduction. Finally, from the fact that for all x_1, x_1 will write a letter if and only if x_1 will play squash, and that for all x_1, x_1 will not play squash we can infer that for all x_1, x_1 will not write a letter via universal biconditional elimination. Therefore, the answer is yes.