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_10, if x_10 takes a plane, then x_10 is working. For all x_10, if x_10 works, then x_10 is a soldier. For all x_10, if x_10 were a soldier, then x_10 is a mechanic. For all x_10, if x_10 takes a plane, then x_10 is a mechanic. For all x_10, if x_10 were a mechanic, then x_10 is taking a plane.
For all x_10, if x_10 takes a plane, then x_10 is a soldier can be inferred via the universal transitivity rule. For all x_10, if x_10 works, then x_10 is a mechanic can be inferred via the universal transitivity rule. For all x_10, if x_10 were a soldier, then x_10 is taking a plane can be inferred via the universal transitivity rule. For all x_10, if x_10 were a mechanic, then x_10 is working can be inferred via the universal transitivity rule. For all x_10, x_10 will take a plane if and only if x_10 is a mechanic can be inferred via the universal biconditional introduction rule. For all x_10, x_10 is a mechanic if and only if x_10 will take a plane can be inferred via the universal biconditional introduction rule.