Consider the following premises. John is drinking water if and only if it is cloudy. If Mary climbs a mountain, then John is drinking water. Mary is climbing a mountain or it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: John is drinking water.
 From the fact that John is drinking water if and only if it is cloudy we can infer that if it is cloudy, then John is drinking water via biconditional elimination. Finally, from the fact that if Mary climbs a mountain, then John is drinking water, that if it is cloudy, then John is drinking water, and that Mary is climbing a mountain or it is cloudy we can infer that John is drinking water via disjunction elimination. Therefore, the answer is yes.