Consider the following premises. For all x_13, if x_13 climbs a mountain, then x_13 is running. For all x_13, if x_13 goes running, then x_13 is climbing a mountain. Charles is climbing a mountain or Charles is not running. Can we infer the following from them? If we can, name the inference rule being used: Charles is running if and only if Charles is climbing a mountain.
 From the fact that for all x_13, if x_13 climbs a mountain, then x_13 is running, and that for all x_13, if x_13 goes running, then x_13 is climbing a mountain we can infer that for all x_13, x_13 will climb a mountain if and only if x_13 will go running via universal biconditional introduction. From the fact that for all x_13, x_13 will climb a mountain if and only if x_13 will go running we can infer that Charles is climbing a mountain if and only if Charles is running via universal instantiation. From the fact that Charles is climbing a mountain or Charles is not running we can infer that if Charles goes running, then Charles is climbing a mountain via rewriting. From the fact that Charles is climbing a mountain if and only if Charles is running we can infer that if Charles climbs a mountain, then Charles is running via biconditional elimination. Finally, from the fact that if Charles goes running, then Charles is climbing a mountain, and that if Charles climbs a mountain, then Charles is running we can infer that Charles is running if and only if Charles is climbing a mountain via biconditional introduction. Therefore, the answer is yes.