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: For all x_2, if x_2 were a doctor, then x_2 is drinking water. For all x_2, x_2 is rich if and only if x_2 is a doctor. There is at least one x_2 for which if x_2 drinks water, then x_2 is writing a letter.
There is at least one x_2 for which if x_2 were a doctor, then x_2 is writing a letter can be inferred via the existential transitivity rule. For all x_2, if x_2 were rich, then x_2 is a doctor can be inferred via the universal biconditional elimination rule. For all x_2, if x_2 were a doctor, then x_2 is rich can be inferred via the universal biconditional elimination rule.