Consider the following premises. It is cloudy if and only if it is overcast. If William plays tennis, then it is cloudy. William is playing tennis or William is not writing a letter. Can we infer the following from them? If we can, name the inference rule being used: If William writes a letter, then it is overcast.
 From the fact that it is cloudy if and only if it is overcast we can infer that if it is cloudy, then it is overcast via biconditional elimination. From the fact that if William plays tennis, then it is cloudy, and that if it is cloudy, then it is overcast we can infer that if William plays tennis, then it is overcast via transitivity. From the fact that William is playing tennis or William is not writing a letter we can infer that if William writes a letter, then William is playing tennis via rewriting. Finally, from the fact that if William writes a letter, then William is playing tennis, and that if William plays tennis, then it is overcast we can infer that if William writes a letter, then it is overcast via transitivity. Therefore, the answer is yes.