Consider the following premises. For all x_7, if x_7 were an artist, then x_7 is curious. There is at least one x_7 for which if x_7 sleeps, then x_7 is an artist. For all x_7, x_7 will sleep or x_7 is not curious. 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 is curious if and only if x_7 will sleep.
 From the fact that for all x_7, x_7 will sleep or x_7 is not curious we can infer that for all x_7, if x_7 were curious, then x_7 is sleeping via universal rewriting. From the fact that there is at least one x_7 for which if x_7 sleeps, then x_7 is an artist, and that for all x_7, if x_7 were an artist, then x_7 is curious we can infer that there is at least one x_7 for which if x_7 sleeps, then x_7 is curious via existential transitivity. Finally, from the fact that for all x_7, if x_7 were curious, then x_7 is sleeping, and that there is at least one x_7 for which if x_7 sleeps, then x_7 is curious we can infer that there is at least one x_7 for which x_7 is curious if and only if x_7 will sleep via existential biconditional introduction. Therefore, the answer is yes.