Consider the following premises. For all x_8, x_8 will write a letter if and only if x_8 will work. There is at least one x_8 for which x_8 will play tennis if and only if x_8 will work. Can we infer the following from them? For all x_8, the fact that x_8 writes a letter does not imply that x_8 is playing tennis.
That contradicts the premises. Therefore the answer is no.