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_1, x_1 is not a mechanic. For all x_1, if x_1 plays tennis, then x_1 is an astronaut. There is at least one x_1 for which if x_1 were an astronaut, then x_1 is playing tennis. For all x_1, x_1 is an astronaut if and only if x_1 is a mechanic.
There is at least one x_1 for which x_1 is an astronaut if and only if x_1 will play tennis can be inferred via the existential biconditional introduction rule. There is at least one x_1 for which x_1 will play tennis if and only if x_1 is an astronaut can be inferred via the existential biconditional introduction rule. For all x_1, if x_1 were an astronaut, then x_1 is a mechanic can be inferred via the universal biconditional elimination rule. For all x_1, if x_1 were a mechanic, then x_1 is an astronaut can be inferred via the universal biconditional elimination rule. For all x_1, x_1 is not an astronaut can be inferred via the universal biconditional elimination rule.