Consider the following premises. For all x_3, if x_3 were an artist, then x_3 is a taxi driver. There is at least one x_3 for which if x_3 were a taxi driver, then x_3 is making tea. For all x_3, if x_3 makes tea, then x_3 is an artist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which if x_3 were a taxi driver, then x_3 is an artist.
We can infer this via the existential transitivity rule. Therefore, the answer is yes.