Consider the following premises. There is at least one x_6 for which if x_6 plays squash, then x_6 is a carpenter. For all x_6, x_6 will play squash if and only if x_6 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which if x_6 were a carpenter, then x_6 is playing squash.
 From the fact that for all x_6, x_6 will play squash if and only if x_6 is a carpenter we can infer that for all x_6, if x_6 were a carpenter, then x_6 is playing squash via universal biconditional elimination. From the fact that for all x_6, if x_6 were a carpenter, then x_6 is playing squash, and that there is at least one x_6 for which if x_6 plays squash, then x_6 is a carpenter we can infer that there is at least one x_6 for which x_6 is a carpenter if and only if x_6 will play squash via existential biconditional introduction. Finally, from the fact that there is at least one x_6 for which x_6 is a carpenter if and only if x_6 will play squash we can infer that there is at least one x_6 for which if x_6 were a carpenter, then x_6 is playing squash via existential biconditional elimination. Therefore, the answer is yes.