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 z_3, if z_3 writes a letter, then z_3 is rich. There is at least one z_3 for which if z_3 were a scientist, then z_3 is rich. For all z_3, if z_3 were rich, then z_3 is writing a letter.
There is at least one z_3 for which if z_3 were a scientist, then z_3 is writing a letter can be inferred via the existential transitivity rule. For all z_3, z_3 will write a letter if and only if z_3 is rich can be inferred via the universal biconditional introduction rule. For all z_3, z_3 is rich if and only if z_3 will write a letter can be inferred via the universal biconditional introduction rule.