Consider the following premises. There is at least one y_4 for which if y_4 drinks water, then y_4 is writing a letter. For all y_4, if y_4 climbs a mountain, then y_4 is drinking water. For all y_4, y_4 will climb a mountain if and only if y_4 will write a letter. Can we infer the following from them? For all y_4, the fact that y_4 climbs a mountain does not imply that y_4 is writing a letter.
That contradicts the premises. Therefore the answer is no.