Consider the following premises. There is at least one x_8 for which x_8 is an astronaut if and only if x_8 will read a book. For all x_8, x_8 will play a game or x_8 will not read a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which if x_8 were an astronaut, then x_8 is playing a game.
 From the fact that there is at least one x_8 for which x_8 is an astronaut if and only if x_8 will read a book we can infer that there is at least one x_8 for which if x_8 were an astronaut, then x_8 is reading a book via existential biconditional elimination. From the fact that for all x_8, x_8 will play a game or x_8 will not read a book we can infer that for all x_8, if x_8 reads a book, then x_8 is playing a game via universal rewriting. Finally, from the fact that there is at least one x_8 for which if x_8 were an astronaut, then x_8 is reading a book, and that for all x_8, if x_8 reads a book, then x_8 is playing a game we can infer that there is at least one x_8 for which if x_8 were an astronaut, then x_8 is playing a game via existential transitivity. Therefore, the answer is yes.