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: Mary is writing a letter if and only if Patricia is a sailor. Karen is not a doctor. If Patricia takes a plane, then Karen is a doctor. For all x_12, x_12 is a sailor if and only if x_12 will take a plane.
Patricia is not taking a plane can be inferred via the modus tollens rule. If Mary writes a letter, then Patricia is a sailor can be inferred via the biconditional elimination rule. If Patricia were a sailor, then Mary is writing a letter can be inferred via the biconditional elimination rule. For all x_12, if x_12 were a sailor, then x_12 is taking a plane can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 takes a plane, then x_12 is a sailor can be inferred via the universal biconditional elimination rule.