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_15, if x_15 plays a game, then x_15 is a mechanic. For all x_15, x_15 will not write a letter. There is at least one x_15 for which x_15 is an electrician if and only if x_15 will work. For all x_15, if x_15 were a mechanic, then x_15 is an electrician. For all x_15, x_15 will write a letter or x_15 will play a game.
For all x_15, if x_15 plays a game, then x_15 is an electrician can be inferred via the universal transitivity rule. For all x_15, x_15 will play a game can be inferred via the universal disjunctive syllogism rule. There is at least one x_15 for which if x_15 were an electrician, then x_15 is working can be inferred via the existential biconditional elimination rule. There is at least one x_15 for which if x_15 works, then x_15 is an electrician can be inferred via the existential biconditional elimination rule.