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: If Elisabeth writes a letter, then Thomas is a cashier. Thomas is a cashier if and only if James is a nurse. If James were a nurse, then Elisabeth is writing a letter. If Thomas were a cashier, then James is a nurse.
If Elisabeth writes a letter, then James is a nurse can be inferred via the transitivity rule. If James were a nurse, then Thomas is a cashier can be inferred via the transitivity rule. If Thomas were a cashier, then Elisabeth is writing a letter can be inferred via the transitivity rule. If Thomas were a cashier, then James is a nurse can be inferred via the biconditional elimination rule. If James were a nurse, then Thomas is a cashier can be inferred via the biconditional elimination rule.