What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: There is at least one y for which if y were a politician, then y is sad. For all y, if y were sad, then y is a doctor. For all y, y is a politician if and only if y is a doctor.
There is at least one y for which if y were a politician, then y is a doctor can be inferred via the existential transitivity rule. For all y, if y were a politician, then y is a doctor can be inferred via the universal biconditional elimination rule. For all y, if y were a doctor, then y is a politician can be inferred via the universal biconditional elimination rule.