Consider the following premises. Mary is an electrician if and only if it is cold. If William goes running, then it is cold. If Jennifer were poor, then William is running. If it is cold, then William is running. Can we infer the following from them? If we can, name the inference rule being used: If Jennifer were poor, then Mary is an electrician.
 From the fact that if William goes running, then it is cold, and that if it is cold, then William is running we can infer that William is running if and only if it is cold via biconditional introduction. From the fact that William is running if and only if it is cold we can infer that if William goes running, then it is cold via biconditional elimination. From the fact that Mary is an electrician if and only if it is cold we can infer that if it is cold, then Mary is an electrician via biconditional elimination. From the fact that if William goes running, then it is cold, and that if it is cold, then Mary is an electrician we can infer that if William goes running, then Mary is an electrician via transitivity. Finally, from the fact that if Jennifer were poor, then William is running, and that if William goes running, then Mary is an electrician we can infer that if Jennifer were poor, then Mary is an electrician via transitivity. Therefore, the answer is yes.