Consider the following premises. For all x_2, if x_2 plays tennis, then x_2 is writing a letter. For all x_2, x_2 is sad. For all x_2, x_2 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 will write a letter.
We can infer this via the universal modus ponens rule. Therefore, the answer is yes.