Consider the following premises. ~r_1. forall x_7: R_7(x_7) <-> S_7(x_7). S_7(g) <-> r_3. r_1 <-> r_3. Can we infer ~R_7(g) from them? If possible, name the inference rules being used at each step.
 From r_1 <-> r_3, ~r_1 we can infer ~r_3 via biconditional elimination. From forall x_7: R_7(x_7) <-> S_7(x_7) we can infer R_7(g) <-> S_7(g) via universal instantiation. From S_7(g) <-> r_3, ~r_3 we can infer ~S_7(g) via biconditional elimination. Finally, from R_7(g) <-> S_7(g), ~S_7(g) we can infer ~R_7(g) via biconditional elimination. Therefore, the answer is yes.