Consider the following premises. For all x_6, x_6 is a bartender or x_6 is not an electrician. There is at least one x_6 for which if x_6 were a poet, then x_6 is an electrician. For all x_6, if x_6 were a bartender, then x_6 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which if x_6 were a poet, then x_6 is playing a game.
 From the fact that for all x_6, x_6 is a bartender or x_6 is not an electrician we can infer that for all x_6, if x_6 were an electrician, then x_6 is a bartender via universal rewriting. From the fact that for all x_6, if x_6 were an electrician, then x_6 is a bartender, and that for all x_6, if x_6 were a bartender, then x_6 is playing a game we can infer that for all x_6, if x_6 were an electrician, then x_6 is playing a game via universal transitivity. Finally, from the fact that there is at least one x_6 for which if x_6 were a poet, then x_6 is an electrician, and that for all x_6, if x_6 were an electrician, then x_6 is playing a game we can infer that there is at least one x_6 for which if x_6 were a poet, then x_6 is playing a game via existential transitivity. Therefore, the answer is yes.