Consider the following premises. Robert is playing a game if and only if Richard is sleeping. Robert is not playing a game. For all x_7, x_7 will sleep if and only if x_7 is an artist. Can we infer the following from them? If we can, name the inference rule being used: Richard is not an artist.
 From the fact that for all x_7, x_7 will sleep if and only if x_7 is an artist we can infer that Richard is sleeping if and only if Richard is an artist via universal instantiation. From the fact that Robert is playing a game if and only if Richard is sleeping, and that Robert is not playing a game we can infer that Richard is not sleeping via biconditional elimination. Finally, from the fact that Richard is sleeping if and only if Richard is an artist, and that Richard is not sleeping we can infer that Richard is not an artist via biconditional elimination. Therefore, the answer is yes.