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: If Joseph writes a letter, then Charles is poor. Charles is poor if and only if Thomas is playing tennis. For all y_1, y_1 will not play tennis.
If Charles were poor, then Thomas is playing tennis can be inferred via the biconditional elimination rule. If Thomas plays tennis, then Charles is poor can be inferred via the biconditional elimination rule.