Consider the following premises. For all x_7, x_7 will climb a mountain if and only if x_7 is curious. For all x_7, if x_7 climbs a mountain, then x_7 is curious. Can we infer the following from them? For all x_7, x_7 will climb a mountain if and only if x_7 is curious.
That is one of the premises. Therefore, the answer is yes.