Consider the following premises. If William plays squash, then Joseph is running. William is playing squash or Elisabeth is not sad. Elisabeth is sad or Joseph is not running. Can we infer the following from them? If we can, name the inference rule being used: Joseph is running if and only if Elisabeth is sad.
 From the fact that William is playing squash or Elisabeth is not sad we can infer that if Elisabeth were sad, then William is playing squash via rewriting. From the fact that Elisabeth is sad or Joseph is not running we can infer that if Joseph goes running, then Elisabeth is sad via rewriting. From the fact that if Elisabeth were sad, then William is playing squash, and that if William plays squash, then Joseph is running we can infer that if Elisabeth were sad, then Joseph is running via transitivity. Finally, from the fact that if Joseph goes running, then Elisabeth is sad, and that if Elisabeth were sad, then Joseph is running we can infer that Joseph is running if and only if Elisabeth is sad via biconditional introduction. Therefore, the answer is yes.