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_3, if x_3 plays squash, then x_3 is cooking. For all x_3, if x_3 cooks, then x_3 is taking a plane. There is at least one x_3 for which x_3 will take a plane if and only if x_3 is an astronaut.
For all x_3, if x_3 plays squash, then x_3 is taking a plane can be inferred via the universal transitivity rule. There is at least one x_3 for which if x_3 takes a plane, then x_3 is an astronaut can be inferred via the existential biconditional elimination rule. There is at least one x_3 for which if x_3 were an astronaut, then x_3 is taking a plane can be inferred via the existential biconditional elimination rule.