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, if x takes a plane, then x is excited. For all x, if x were excited, then x is taking a plane. For all x, x will not take a plane. There is at least one x for which x is excited if and only if x will read a book.
For all x, x is not excited can be inferred via the universal modus tollens rule. For all x, x will take a plane if and only if x is excited can be inferred via the universal biconditional introduction rule. For all x, x is excited if and only if x will take a plane can be inferred via the universal biconditional introduction rule. There is at least one x for which if x were excited, then x is reading a book can be inferred via the existential biconditional elimination rule. There is at least one x for which if x reads a book, then x is excited can be inferred via the existential biconditional elimination rule.