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 a lawyer if and only if x_13 is excited. For all x_13, x_13 will go running. For all x_13, if x_13 goes running, then x_13 is a lawyer. For all x_13, x_13 is excited if and only if x_13 is a writer.
For all x_13, x_13 is a lawyer can be inferred via the universal modus ponens rule. For all x_13, if x_13 were a lawyer, then x_13 is excited can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were excited, then x_13 is a writer can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were excited, then x_13 is a lawyer can be inferred via the universal biconditional elimination rule. For all x_13, if x_13 were a writer, then x_13 is excited can be inferred via the universal biconditional elimination rule.