Consider the following premises. If David were an astronaut, then David is an artist. If it is cold, then David is an astronaut. David is not an artist. For all x_12, if x_12 were an artist, then x_12 is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that for all x_12, if x_12 were an artist, then x_12 is an astronaut we can infer that if David were an artist, then David is an astronaut via universal instantiation. From the fact that if David were an artist, then David is an astronaut, and that if David were an astronaut, then David is an artist we can infer that David is an artist if and only if David is an astronaut via biconditional introduction. From the fact that David is an artist if and only if David is an astronaut, and that David is not an artist we can infer that David is not an astronaut via biconditional elimination. Finally, from the fact that if it is cold, then David is an astronaut, and that David is not an astronaut we can infer that it is not cold via modus tollens. Therefore, the answer is yes.