Almost. Its answer is a direct consequence of Rice's theorem (“A Turing machine can't decide non-trivial properties on Turing machines given as input”), which i

Almost. Its answer is a direct consequence of Rice's theorem (“A Turing machine can't decide non-trivial properties on Turing machines given as input”), which is itself proven using the undecidability of the Halting Problem (“A Turing Machine can't decide whether Turing Machines given as input stop.”).