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, if x were an electrician, then x is an astronaut. For all x, if x were a musician, then x is an office clerk. For all x, if x were an astronaut, then x is a musician. For all x, if x were an office clerk, then x is a musician. For all x, x is an electrician.
For all x, x is an astronaut can be inferred via the universal modus ponens rule. For all x, if x were an electrician, then x is a musician can be inferred via the universal transitivity rule. For all x, if x were an astronaut, then x is an office clerk can be inferred via the universal transitivity rule. For all x, x is a musician if and only if x is an office clerk can be inferred via the universal biconditional introduction rule. For all x, x is an office clerk if and only if x is a musician can be inferred via the universal biconditional introduction rule.