We demonstrate efficient subthermal cooling of the modified cyclotron mode of a single trapped antiproton and reach particle temperatures T_{+}=E_{+}/k_{B} below 200 mK in preparation times shorter than 500 s. This corresponds to the fastest resistive single-particle cyclotron cooling to subthermal temperatures ever demonstrated. By cooling trapped particles to such low energies, we demonstrate the detection of antiproton spin transitions with an error rate <0.000 023, more than 3 orders …