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: There is at least one x for which x is a doctor if and only if x will write a letter. For all x, if x were a doctor, then x is making tea. For all x, if x makes tea, then x is a musician.
For all x, if x were a doctor, then x is a musician can be inferred via the universal transitivity rule. There is at least one x for which if x were a doctor, then x is writing a letter can be inferred via the existential biconditional elimination rule. There is at least one x for which if x writes a letter, then x is a doctor can be inferred via the existential biconditional elimination rule.