Consider the following premises. There is at least one y_1 for which y_1 will play squash if and only if y_1 will climb a mountain. For all y_1, y_1 will not cook. For all y_1, if y_1 plays squash, then y_1 is playing tennis. For all y_1, y_1 will play tennis if and only if y_1 will cook. Can we infer the following from them? For all y_1, if y_1 plays squash, then y_1 is playing tennis.
That is one of the premises. Therefore, the answer is yes.