Consider the following premises. For all x_7, x_7 is a mechanic or x_7 is sad. For all x_7, if x_7 were a mechanic, then x_7 is reading a book. For all x_7, x_7 is sad if and only if x_7 will play a game. For all x_7, if x_7 reads a book, then x_7 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, if x_7 reads a book, then x_7 is playing a game.
That is one of the premises. Therefore, the answer is yes.