Consider the following premises. For all x_6, if x_6 were a lawyer, then x_6 is working. There is at least one x_6 for which if x_6 listens to a song, then x_6 is working. For all x_6, if x_6 works, then x_6 is listening 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_6 for which if x_6 were a lawyer, then x_6 is listening to a song.
 From the fact that there is at least one x_6 for which if x_6 listens to a song, then x_6 is working, and that for all x_6, if x_6 works, then x_6 is listening to a song we can infer that there is at least one x_6 for which x_6 will listen to a song if and only if x_6 will work via existential biconditional introduction. From the fact that there is at least one x_6 for which x_6 will listen to a song if and only if x_6 will work we can infer that there is at least one x_6 for which if x_6 works, then x_6 is listening to a song via existential biconditional elimination. Finally, from the fact that for all x_6, if x_6 were a lawyer, then x_6 is working, and that there is at least one x_6 for which if x_6 works, then x_6 is listening to a song we can infer that there is at least one x_6 for which if x_6 were a lawyer, then x_6 is listening to a song via existential transitivity. Therefore, the answer is yes.