Consider the following premises. For all y, if y climbs a mountain, then y is a taxi driver. There is at least one y for which if y were a taxi driver, then y is climbing a mountain. For all y, if y climbs a mountain, then y is a taxi driver. Can we infer the following from them? For all y, if y climbs a mountain, then y is a taxi driver.
That is one of the premises. Therefore, the answer is yes.