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_13, x_13 is rich if and only if x_13 will write a letter. For all x_13, if x_13 writes a letter, then x_13 is rich. For all x_13, x_13 is rich if and only if x_13 is a scientist. For all x_13, x_13 is not a scientist.
For all x_13, if x_13 were rich, then x_13 is writing a letter can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were rich, then x_13 is a scientist can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 writes a letter, then x_13 is rich can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were a scientist, then x_13 is rich can be inferred via the universal biconditional elimination rule. For all x_13, x_13 is not rich can be inferred via the universal biconditional elimination rule.