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_15, x_15 is a mechanic if and only if x_15 will write a letter. For all x_15, if x_15 were a mechanic, then x_15 is an astronaut. There is at least one x_15 for which x_15 will write a letter if and only if x_15 is an astronaut.
For all x_15, if x_15 were a mechanic, then x_15 is writing a letter can be inferred via the universal biconditional elimination rule. There is at least one x_15 for which if x_15 writes a letter, then x_15 is an astronaut can be inferred via the existential biconditional elimination rule. For all x_15, if x_15 writes a letter, then x_15 is a mechanic can be inferred via the universal biconditional elimination rule. There is at least one x_15 for which if x_15 were an astronaut, then x_15 is writing a letter can be inferred via the existential biconditional elimination rule.