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$^{-1/2}$.
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