Consider the following premises. For all z, if z sleeps, then z is drinking water. For all z, if z were excited, then z is sleeping. If Michael drinks water, then David is playing a game. If David plays a game, then Michael is excited. Can we infer the following from them? Michael is excited if and only if Michael is drinking water.
 From the fact that for all z, if z were excited, then z is sleeping, and that for all z, if z sleeps, then z is drinking water we can infer that for all z, if z were excited, then z is drinking water. From the fact that for all z, if z were excited, then z is drinking water we can infer that if Michael were excited, then Michael is drinking water. From the fact that if Michael drinks water, then David is playing a game, and that if David plays a game, then Michael is excited we can infer that if Michael drinks water, then Michael is excited. Finally, from the fact that if Michael were excited, then Michael is drinking water, and that if Michael drinks water, then Michael is excited we can infer that Michael is excited if and only if Michael is drinking water. Therefore, the answer is yes.