Consider the following premises. There is at least one x_3 for which if x_3 listens to a song, then x_3 is a server. For all x_3, if x_3 were a server, then x_3 is rich. For all x_3, x_3 is rich if and only if x_3 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which if x_3 were rich, then x_3 is listening to a song.
 From the fact that there is at least one x_3 for which if x_3 listens to a song, then x_3 is a server, and that for all x_3, if x_3 were a server, then x_3 is rich we can infer that there is at least one x_3 for which if x_3 listens to a song, then x_3 is rich via existential transitivity. From the fact that for all x_3, x_3 is rich if and only if x_3 will listen to a song we can infer that for all x_3, if x_3 were rich, then x_3 is listening to a song via universal biconditional elimination. From the fact that there is at least one x_3 for which if x_3 listens to a song, then x_3 is rich, and that for all x_3, if x_3 were rich, then x_3 is listening to a song we can infer that there is at least one x_3 for which x_3 will listen to a song if and only if x_3 is rich via existential biconditional introduction. Finally, from the fact that there is at least one x_3 for which x_3 will listen to a song if and only if x_3 is rich we can infer that there is at least one x_3 for which if x_3 were rich, then x_3 is listening to a song via existential biconditional elimination. Therefore, the answer is yes.