Consider the following premises. Richard is a bartender. Elisabeth is a soldier if and only if it is cloudy. It is cloudy. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not a soldier.
 From the fact that Elisabeth is a soldier if and only if it is cloudy we can infer that if it is cloudy, then Elisabeth is a soldier via biconditional elimination. Finally, from the fact that if it is cloudy, then Elisabeth is a soldier, and that it is cloudy we can infer that Elisabeth is a soldier via modus ponens, which contradicts that Elisabeth is not a soldier. Therefore, the answer is no.