Consider the following premises. For all x_11, if x_11 were a doctor, then x_11 is listening to a song. There is at least one x_11 for which if x_11 were bored, then x_11 is a doctor. For all x_11, x_11 is bored if and only if x_11 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_11 for which if x_11 were bored, then x_11 is listening to a song.
 From the fact that for all x_11, x_11 is bored if and only if x_11 will listen to a song we can infer that for all x_11, if x_11 listens to a song, then x_11 is bored via universal biconditional elimination. Finally, from the fact that there is at least one x_11 for which if x_11 were bored, then x_11 is a doctor, and that for all x_11, if x_11 were a doctor, then x_11 is listening to a song we can infer that there is at least one x_11 for which if x_11 were bored, then x_11 is listening to a song via existential transitivity. Therefore, the answer is yes.