Consider the following premises. For all x_9, x_9 will drink water if and only if x_9 is rich. Mary is not rich. If Mary drinks water, then Mary is rich. Can we infer the following from them? If we can, name the inference rule being used: Mary is drinking water.
 From the fact that for all x_9, x_9 will drink water if and only if x_9 is rich we can infer that Mary is drinking water if and only if Mary is rich via universal instantiation. From the fact that Mary is drinking water if and only if Mary is rich we can infer that if Mary were rich, then Mary is drinking water via biconditional elimination. From the fact that if Mary drinks water, then Mary is rich, and that if Mary were rich, then Mary is drinking water we can infer that Mary is drinking water if and only if Mary is rich via biconditional introduction. Finally, from the fact that Mary is drinking water if and only if Mary is rich, and that Mary is not rich we can infer that Mary is not drinking water via biconditional elimination, which contradicts that Mary is drinking water. Therefore, the answer is no.