Consider the following premises. For all y, if y were a sailor, then y is a doctor. For all y, if y were a bartender, then y is a sailor. For all y, if y were a doctor, then y is a bartender. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which the fact that y were a sailor does not imply that y is a doctor.
 From the fact that for all y, if y were a doctor, then y is a bartender, and that for all y, if y were a bartender, then y is a sailor we can infer that for all y, if y were a doctor, then y is a sailor via universal transitivity. From the fact that for all y, if y were a sailor, then y is a doctor, and that for all y, if y were a doctor, then y is a sailor we can infer that for all y, y is a sailor if and only if y is a doctor via universal biconditional introduction. Finally, from the fact that for all y, y is a sailor if and only if y is a doctor we can infer that for all y, if y were a sailor, then y is a doctor via universal biconditional elimination, which contradicts that There is at least one y for which the fact that y were a sailor does not imply that y is a doctor. Therefore, the answer is no.