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: Joseph is not a carpenter. For all x_12, if x_12 writes a letter, then x_12 is a carpenter. If Joseph doesn't write a letter, then Thomas is playing squash. For all x_12, if x_12 were a carpenter, then x_12 is writing a letter.
For all x_12, x_12 will write a letter if and only if x_12 is a carpenter can be inferred via the universal biconditional introduction rule. For all x_12, x_12 is a carpenter if and only if x_12 will write a letter can be inferred via the universal biconditional introduction rule.