Consider the following premises. For all x_5, x_5 will climb a mountain if and only if x_5 will go running. For all x_5, if x_5 climbs a mountain, then x_5 is running. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, if x_5 climbs a mountain, then x_5 is running.
That is one of the premises. Therefore, the answer is yes.