Consider the following premises. For all x_10, x_10 is not a lawyer. It is raining if and only if it is cloudy. It is raining if and only if Sarah is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: It is not cloudy.
 From the fact that for all x_10, x_10 is not a lawyer we can infer that Sarah is not a lawyer via universal instantiation. From the fact that it is raining if and only if Sarah is a lawyer, and that Sarah is not a lawyer we can infer that it is not raining via biconditional elimination. Finally, from the fact that it is raining if and only if it is cloudy, and that it is not raining we can infer that it is not cloudy via biconditional elimination. Therefore, the answer is yes.