Consider the following premises. Thomas is a mechanic if and only if Michael is sad. Thomas is a mechanic or Michael is not sad. Can we infer the following from them? If Thomas were a mechanic, then Michael is sad.
 From the fact that Thomas is a mechanic or Michael is not sad we can infer that if Michael were sad, then Thomas is a mechanic. Finally, from the fact that Thomas is a mechanic if and only if Michael is sad we can infer that if Thomas were a mechanic, then Michael is sad. Therefore, the answer is yes.