Consider the following premises. Joseph is not fast. If it is sunny, then Joseph is fast. If Joseph were fast, then it is sunny. If it is not sunny, then it is cold. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that if Joseph were fast, then it is sunny, and that if it is sunny, then Joseph is fast we can infer that Joseph is fast if and only if it is sunny via biconditional introduction. From the fact that Joseph is fast if and only if it is sunny, and that Joseph is not fast we can infer that it is not sunny via biconditional elimination. Finally, from the fact that if it is not sunny, then it is cold, and that it is not sunny we can infer that it is cold via modus ponens, which contradicts that It is not cold. Therefore, the answer is no.