Consider the following premises. If Michael drinks water, then Michael is a musician. For all x_7, x_7 will drink water or x_7 is not a musician. Can we infer the following from them? If we can, name the inference rule being used: Michael is a musician if and only if Michael is drinking water.
 From the fact that for all x_7, x_7 will drink water or x_7 is not a musician we can infer that for all x_7, if x_7 were a musician, then x_7 is drinking water via universal rewriting. From the fact that for all x_7, if x_7 were a musician, then x_7 is drinking water we can infer that if Michael were a musician, then Michael is drinking water via universal instantiation. Finally, from the fact that if Michael were a musician, then Michael is drinking water, and that if Michael drinks water, then Michael is a musician we can infer that Michael is a musician if and only if Michael is drinking water via biconditional introduction. Therefore, the answer is yes.