Consider the following premises. For all x_7, if x_7 sleeps, then x_7 is a poet. For all x_7, if x_7 were a poet, then x_7 is sleeping. There is at least one x_7 for which if x_7 sleeps, then x_7 is a poet. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will sleep if and only if x_7 is a poet.
 From the fact that for all x_7, if x_7 were a poet, then x_7 is sleeping, and that there is at least one x_7 for which if x_7 sleeps, then x_7 is a poet we can infer that there is at least one x_7 for which x_7 is a poet if and only if x_7 will sleep via existential biconditional introduction. From the fact that there is at least one x_7 for which x_7 is a poet if and only if x_7 will sleep we can infer that there is at least one x_7 for which if x_7 were a poet, then x_7 is sleeping via existential biconditional elimination. Finally, from the fact that for all x_7, if x_7 sleeps, then x_7 is a poet, and that there is at least one x_7 for which if x_7 were a poet, then x_7 is sleeping we can infer that there is at least one x_7 for which x_7 will sleep if and only if x_7 is a poet via existential biconditional introduction. Therefore, the answer is yes.