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_6, if x_6 were a musician, then x_6 is writing a letter. For all x_6, if x_6 were happy, then x_6 is writing a letter. There is at least one x_6 for which if x_6 were a musician, then x_6 is happy. For all x_6, if x_6 writes a letter, then x_6 is a musician.
For all x_6, if x_6 were happy, then x_6 is a musician can be inferred via the universal transitivity rule. There is at least one x_6 for which if x_6 were a musician, then x_6 is writing a letter can be inferred via the existential transitivity rule. There is at least one x_6 for which if x_6 writes a letter, then x_6 is happy can be inferred via the existential transitivity rule. For all x_6, x_6 is a musician if and only if x_6 will write a letter can be inferred via the universal biconditional introduction rule. For all x_6, x_6 will write a letter if and only if x_6 is a musician can be inferred via the universal biconditional introduction rule.