Consider the following premises. If John were sad, then John is a bartender. For all y_4, y_4 is sad if and only if y_4 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: The fact that John were a bartender does not imply that John is sad.
 From the fact that for all y_4, y_4 is sad if and only if y_4 is a bartender we can infer that John is sad if and only if John is a bartender via universal instantiation. Finally, from the fact that John is sad if and only if John is a bartender we can infer that if John were a bartender, then John is sad via biconditional elimination, which contradicts that The fact that John were a bartender does not imply that John is sad. Therefore, the answer is no.