Consider the following premises. For all x_8, x_8 will listen to a song and x_8 is an electrician. For all x_8, x_8 will climb a mountain if and only if x_8 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will climb a mountain.
 From the fact that for all x_8, x_8 will climb a mountain if and only if x_8 will listen to a song we can infer that for all x_8, if x_8 listens to a song, then x_8 is climbing a mountain via universal biconditional elimination. From the fact that for all x_8, x_8 will listen to a song and x_8 is an electrician we can infer that for all x_8, x_8 will listen to a song via universal simplification. Finally, from the fact that for all x_8, if x_8 listens to a song, then x_8 is climbing a mountain, and that for all x_8, x_8 will listen to a song we can infer that for all x_8, x_8 will climb a mountain via universal modus ponens. Therefore, the answer is yes.