Consider the following premises. If Charles works, then it is cold. It is cold if and only if it is raining. It is raining or John is happy. John is happy if and only if Charles is working. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that John is happy if and only if Charles is working we can infer that if John were happy, then Charles is working via biconditional elimination. From the fact that if John were happy, then Charles is working, and that if Charles works, then it is cold we can infer that if John were happy, then it is cold via transitivity. From the fact that it is cold if and only if it is raining we can infer that if it rains, then it is cold via biconditional elimination. Finally, from the fact that if it rains, then it is cold, that if John were happy, then it is cold, and that it is raining or John is happy we can infer that it is cold via disjunction elimination, which contradicts that It is not cold. Therefore, the answer is no.