Consider the following premises. There is at least one y for which if y cooks, then y is happy. For all y, if y were happy, then y is playing tennis. For all y, y will climb a mountain if and only if y will play tennis. Can we infer the following from them? For all y, the fact that y cooks does not imply that y is climbing a mountain.
That contradicts the premises. Therefore the answer is no.