Consider the following premises. Richard is writing a letter or it is sunny. Richard is not sleeping. For all x_7, x_7 will write a letter if and only if x_7 will sleep. Can we infer the following from them? If we can, name the inference rule being used: It is sunny.
 From the fact that for all x_7, x_7 will write a letter if and only if x_7 will sleep we can infer that Richard is writing a letter if and only if Richard is sleeping via universal instantiation. From the fact that Richard is writing a letter if and only if Richard is sleeping, and that Richard is not sleeping we can infer that Richard is not writing a letter via biconditional elimination. Finally, from the fact that Richard is writing a letter or it is sunny, and that Richard is not writing a letter we can infer that it is sunny via disjunctive syllogism. Therefore, the answer is yes.