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_10, x_10 will not play a game. For all x_12, x_12 is a writer if and only if x_12 is a politician. If Joseph were a politician, then Patricia is playing a game.
For all x_12, if x_12 were a writer, then x_12 is a politician can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 were a politician, then x_12 is a writer can be inferred via the universal biconditional elimination rule.