Consider the following premises. If it is cloudy, then John is a politician. If John were a politician, then it is sunny. If it is sunny, then it is cloudy. It is sunny if and only if it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: If is not true that it is sunny if and only if John is a politician.
 From the fact that it is sunny if and only if it is cloudy we can infer that if it is cloudy, then it is sunny via biconditional elimination. From the fact that if it is sunny, then it is cloudy, and that if it is cloudy, then it is sunny we can infer that it is sunny if and only if it is cloudy via biconditional introduction. From the fact that it is sunny if and only if it is cloudy we can infer that if it is sunny, then it is cloudy via biconditional elimination. From the fact that if it is sunny, then it is cloudy, and that if it is cloudy, then John is a politician we can infer that if it is sunny, then John is a politician via transitivity. Finally, from the fact that if it is sunny, then John is a politician, and that if John were a politician, then it is sunny we can infer that it is sunny if and only if John is a politician via biconditional introduction, which contradicts that If is not true that it is sunny if and only if John is a politician. Therefore, the answer is no.