Consider the following premises. For all x_7, x_7 is an electrician if and only if x_7 is an astronaut. Barbara is a mechanic if and only if it is snowing. Barbara is a mechanic if and only if Michael is an astronaut. It is not snowing. Can we infer the following from them? Michael is not an electrician.
 From the fact that Barbara is a mechanic if and only if it is snowing, and that it is not snowing we can infer that Barbara is not a mechanic. From the fact that for all x_7, x_7 is an electrician if and only if x_7 is an astronaut we can infer that Michael is an electrician if and only if Michael is an astronaut. From the fact that Barbara is a mechanic if and only if Michael is an astronaut, and that Barbara is not a mechanic we can infer that Michael is not an astronaut. Finally, from the fact that Michael is an electrician if and only if Michael is an astronaut, and that Michael is not an astronaut we can infer that Michael is not an electrician. Therefore, the answer is yes.