Consider the following premises. Mary is happy if and only if Patricia is running. James is a lawyer or Mary is not happy. Can we infer the following from them? If we can, name the inference rule being used: If Patricia goes running, then James is a lawyer.
 From the fact that James is a lawyer or Mary is not happy we can infer that if Mary were happy, then James is a lawyer via rewriting. From the fact that Mary is happy if and only if Patricia is running we can infer that if Patricia goes running, then Mary is happy via biconditional elimination. Finally, from the fact that if Patricia goes running, then Mary is happy, and that if Mary were happy, then James is a lawyer we can infer that if Patricia goes running, then James is a lawyer via transitivity. Therefore, the answer is yes.