Consider the following premises. For all x_3, x_3 is not a mechanic. For all x_3, x_3 will play squash or x_3 is not a mechanic. For all x_3, if x_3 plays squash, then x_3 is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, x_3 will not play squash.
 From the fact that for all x_3, x_3 will play squash or x_3 is not a mechanic we can infer that for all x_3, if x_3 were a mechanic, then x_3 is playing squash via universal rewriting. From the fact that for all x_3, if x_3 were a mechanic, then x_3 is playing squash, and that for all x_3, if x_3 plays squash, then x_3 is a mechanic we can infer that for all x_3, x_3 is a mechanic if and only if x_3 will play squash via universal biconditional introduction. Finally, from the fact that for all x_3, x_3 is a mechanic if and only if x_3 will play squash, and that for all x_3, x_3 is not a mechanic we can infer that for all x_3, x_3 will not play squash via universal biconditional elimination. Therefore, the answer is yes.