Consider the following premises. For all x_7, if x_7 were a nurse, then x_7 is bored. For all x_7, if x_7 plays tennis, then x_7 is a nurse. For all x_7, if x_7 were bored, then x_7 is sleeping. There is at least one x_7 for which if x_7 sleeps, then x_7 is playing tennis. Can we infer the following from them? There is at least one x_7 for which if x_7 sleeps, then x_7 is playing tennis.
That is one of the premises. Therefore, the answer is yes.