Consider the following premises. For all x_14, x_14 will cook if and only if x_14 is a doctor. Thomas is a doctor if and only if Thomas is cooking. Can we infer the following from them? If we can, name the inference rule being used: The fact that Thomas were a doctor does not imply that Thomas is cooking.
 From the fact that for all x_14, x_14 will cook if and only if x_14 is a doctor we can infer that Thomas is cooking if and only if Thomas is a doctor via universal instantiation. From the fact that Thomas is a doctor if and only if Thomas is cooking we can infer that if Thomas cooks, then Thomas is a doctor via biconditional elimination. Finally, from the fact that Thomas is cooking if and only if Thomas is a doctor we can infer that if Thomas were a doctor, then Thomas is cooking via biconditional elimination, which contradicts that The fact that Thomas were a doctor does not imply that Thomas is cooking. Therefore, the answer is no.