Consider the following premises. For all y_2, y_2 will write a letter. For all y_2, y_2 is a doctor or y_2 is sad. For all y_2, if y_2 were sad, then y_2 is a sailor. For all y_2, y_2 is a doctor if and only if y_2 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: For all y_2, y_2 will write a letter.
That is one of the premises. Therefore, the answer is yes.