  Dual-frequency comb spectroscopy has emerged as a disruptive technique for
measuring wide-spanning spectra with high resolution, yielding a particularly
powerful technique for sensitive multi-component gas analysis. We present a
spectrometer system based on dual electro-optical combs with subsequent
conversion to the mid-infrared via tunable difference frequency generation,
operating in the range from 3 to 4.7 $\mu$m. The simultaneously recorded
bandwidth is up to 454(1) GHz and a signal-to-noise ratio of 7.3(2) x 10$^2$
Hz$^{-1/2}$ can be reached. The conversion preserves the coherence of the
dual-comb within 3 s measurement time. Concentration measurements of 5 ppm
methane at 3.3 $\mu$m, 100 ppm nitrous oxide at 3.9 $\mu$m and a mixture of 15
ppm carbon monoxide and 5 % carbon dioxide at 4.5 $\mu$m are presented with a
relative precision of 1.4 % in average after 2 s measurement time. The
noise-equivalent absorbance is determined to be less than 4.6(2) x 10$^{-3}$
Hz$^{-1/2}$.
