Consider the following premises. It is cold if and only if John is fast. It is late or John is fast. If it is late, then Charles is a lawyer. If it is cold, then Charles is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: Charles is a lawyer or Michael is running.
 From the fact that it is cold if and only if John is fast we can infer that if John were fast, then it is cold via biconditional elimination. From the fact that if John were fast, then it is cold, and that if it is cold, then Charles is a lawyer we can infer that if John were fast, then Charles is a lawyer via transitivity. From the fact that if it is late, then Charles is a lawyer, that if John were fast, then Charles is a lawyer, and that it is late or John is fast we can infer that Charles is a lawyer via disjunction elimination. Finally, from the fact that Charles is a lawyer we can infer that Charles is a lawyer or Michael is running via addition. Therefore, the answer is yes.