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: William is a nurse if and only if John is a mechanic. William is a nurse if and only if Patricia is a server. John is not a mechanic. For all x_3, x_3 is a server if and only if x_3 will work.
If William were a nurse, then John is a mechanic can be inferred via the biconditional elimination rule. If William were a nurse, then Patricia is a server can be inferred via the biconditional elimination rule. If John were a mechanic, then William is a nurse can be inferred via the biconditional elimination rule. If Patricia were a server, then William is a nurse can be inferred via the biconditional elimination rule. William is not a nurse can be inferred via the biconditional elimination rule. For all x_3, if x_3 were a server, then x_3 is working can be inferred via the universal biconditional elimination rule. For all x_3, if x_3 works, then x_3 is a server can be inferred via the universal biconditional elimination rule.