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_17, if x_17 were an electrician, then x_17 is writing a letter. There is at least one x_17 for which x_17 will play a game. For all x_17, if x_17 were a carpenter, then x_17 is not playing a game. For all x_17, if x_17 writes a letter, then x_17 is an electrician. For all x_17, x_17 is a carpenter if and only if x_17 will write a letter.
There is at least one x_17 for which x_17 is not a carpenter can be inferred via the existential modus tollens rule. For all x_17, x_17 is an electrician if and only if x_17 will write a letter can be inferred via the universal biconditional introduction rule. For all x_17, x_17 will write a letter if and only if x_17 is an electrician can be inferred via the universal biconditional introduction rule. For all x_17, if x_17 were a carpenter, then x_17 is writing a letter can be inferred via the universal biconditional elimination rule. For all x_17, if x_17 writes a letter, then x_17 is a carpenter can be inferred via the universal biconditional elimination rule.