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: Joseph is a lawyer if and only if Mary is reading a book. Joseph is a lawyer if and only if Thomas is a bartender. Mary is reading a book or it is raining. Thomas is not a bartender.
If Joseph were a lawyer, then Mary is reading a book can be inferred via the biconditional elimination rule. If Joseph were a lawyer, then Thomas is a bartender can be inferred via the biconditional elimination rule. If Mary reads a book, then Joseph is a lawyer can be inferred via the biconditional elimination rule. If Thomas were a bartender, then Joseph is a lawyer can be inferred via the biconditional elimination rule. Joseph is not a lawyer can be inferred via the biconditional elimination rule.