Consider the following premises. There is at least one x_6 for which if x_6 were a police officer, then x_6 is climbing a mountain. For all x_6, if x_6 climbs a mountain, then x_6 is a police officer. For all x_6, if x_6 climbs a mountain, then x_6 is a police officer. Can we infer the following from them? There is at least one x_6 for which x_6 is a police officer if and only if x_6 will climb a mountain.
Yes.