Consider the following premises. For all x_4, x_4 is a mechanic if and only if x_4 will listen to a song. For all x_4, if x_4 listens to a song, then x_4 is a mechanic. Susan is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 will listen to a song.
 From the fact that for all x_4, x_4 is a mechanic if and only if x_4 will listen to a song we can infer that for all x_4, if x_4 were a mechanic, then x_4 is listening to a song via universal biconditional elimination. From the fact that for all x_4, if x_4 were a mechanic, then x_4 is listening to a song, and that for all x_4, if x_4 listens to a song, then x_4 is a mechanic we can infer that for all x_4, x_4 is a mechanic if and only if x_4 will listen to a song via universal biconditional introduction. From the fact that Susan is a mechanic we can infer that there is at least one x_4 for which x_4 is a mechanic via existential generalization. From the fact that for all x_4, x_4 is a mechanic if and only if x_4 will listen to a song we can infer that for all x_4, if x_4 were a mechanic, then x_4 is listening to a song via universal biconditional elimination. Finally, from the fact that for all x_4, if x_4 were a mechanic, then x_4 is listening to a song, and that there is at least one x_4 for which x_4 is a mechanic we can infer that there is at least one x_4 for which x_4 will listen to a song via existential modus ponens. Therefore, the answer is yes.