Consider the following premises. If James plays squash, then Robert is a nurse. Robert is a nurse if and only if it is cold. If it is cold, then James is playing squash. Robert is not a nurse. Can we infer the following from them? If we can, name the inference rule being used: James is playing squash.
 From the fact that Robert is a nurse if and only if it is cold we can infer that if Robert were a nurse, then it is cold via biconditional elimination. From the fact that if Robert were a nurse, then it is cold, and that if it is cold, then James is playing squash we can infer that if Robert were a nurse, then James is playing squash via transitivity. From the fact that if James plays squash, then Robert is a nurse, and that if Robert were a nurse, then James is playing squash we can infer that James is playing squash if and only if Robert is a nurse via biconditional introduction. Finally, from the fact that James is playing squash if and only if Robert is a nurse, and that Robert is not a nurse we can infer that James is not playing squash via biconditional elimination, which contradicts that James is playing squash. Therefore, the answer is no.