Consider the following premises. For all x_13, if x_13 works, then x_13 is listening to a song. For all x_13, if x_13 goes running, then x_13 is an office clerk. There is at least one x_13 for which x_13 will listen to a song if and only if x_13 will go running. For all x_13, if x_13 were an office clerk, then x_13 is working. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_13 for which x_13 will work if and only if x_13 will go running.
 From the fact that there is at least one x_13 for which x_13 will listen to a song if and only if x_13 will go running we can infer that there is at least one x_13 for which if x_13 listens to a song, then x_13 is running via existential biconditional elimination. From the fact that for all x_13, if x_13 goes running, then x_13 is an office clerk, and that for all x_13, if x_13 were an office clerk, then x_13 is working we can infer that for all x_13, if x_13 goes running, then x_13 is working via universal transitivity. From the fact that for all x_13, if x_13 works, then x_13 is listening to a song, and that there is at least one x_13 for which if x_13 listens to a song, then x_13 is running we can infer that there is at least one x_13 for which if x_13 works, then x_13 is running via existential transitivity. Finally, from the fact that there is at least one x_13 for which if x_13 works, then x_13 is running, and that for all x_13, if x_13 goes running, then x_13 is working we can infer that there is at least one x_13 for which x_13 will work if and only if x_13 will go running via existential biconditional introduction. Therefore, the answer is yes.