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_9, if x_9 were a nurse, then x_9 is an electrician. For all x_9, if x_9 were an electrician, then x_9 is a nurse. There is at least one x_9 for which x_9 will not write a letter. For all x_9, if x_9 were a nurse, then x_9 is writing a letter.
There is at least one x_9 for which x_9 is not a nurse can be inferred via the existential modus tollens rule. For all x_9, if x_9 were an electrician, then x_9 is writing a letter can be inferred via the universal transitivity rule. For all x_9, x_9 is a nurse if and only if x_9 is an electrician can be inferred via the universal biconditional introduction rule. For all x_9, x_9 is an electrician if and only if x_9 is a nurse can be inferred via the universal biconditional introduction rule.