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 y, if y were an astronaut, then y is a poet. For all y, if y were a poet, then y is an astronaut. For all y, y will go running if and only if y is a poet. For all y, y will not go running.
For all y, y is an astronaut if and only if y is a poet can be inferred via the universal biconditional introduction rule. For all y, y is a poet if and only if y is an astronaut can be inferred via the universal biconditional introduction rule. For all y, if y goes running, then y is a poet can be inferred via the universal biconditional elimination rule. For all y, if y were a poet, then y is running can be inferred via the universal biconditional elimination rule. For all y, y is not a poet can be inferred via the universal biconditional elimination rule.