Consider the following premises. For all x_6, x_6 will play a game or x_6 is a musician. For all x_6, if x_6 were happy, then x_6 is writing a letter. For all x_6, if x_6 were a musician, then x_6 is happy. For all x_6, if x_6 were sad, then x_6 is writing a letter. For all x_6, if x_6 plays a game, then x_6 is happy. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will write a letter.
 From the fact that for all x_6, if x_6 plays a game, then x_6 is happy, that for all x_6, if x_6 were a musician, then x_6 is happy, and that for all x_6, x_6 will play a game or x_6 is a musician we can infer that for all x_6, x_6 is happy via universal disjunction elimination. From the fact that for all x_6, x_6 is happy we can infer that for all x_6, x_6 is happy or x_6 is sad via universal addition. Finally, from the fact that for all x_6, if x_6 were happy, then x_6 is writing a letter, that for all x_6, if x_6 were sad, then x_6 is writing a letter, and that for all x_6, x_6 is happy or x_6 is sad we can infer that for all x_6, x_6 will write a letter via universal disjunction elimination. Therefore, the answer is yes.