We report the discovery of the relatively bright (V = 10.5 mag), doubly eclipsing 2+2 quadruple system CzeV1731. This is the third known system of its kind, in which the masses are determined for all four stars and both the inner and outer orbits are characterized. The inner eclipsing binaries are well-detached systems moving on circular orbits: pair A with period P_A = 4.10843 d and pair B with P_B = 4.67552 d. The inner binaries contain very similar components (q ≈ 1.0), making the whole system a so-called double twin. The stars in pair B have slightly larger luminosities and masses and pair A shows deeper eclipses. All four components are main-sequence stars of F/G spectral type. The mutual orbit of the two pairs around the system barycenter has a period of about 34 yr and an eccentricity of about 0.38. However, further observations are needed to reveal the overall architecture of the whole system, including the mutual inclinations of all orbits. This is a promising target for interferometry to detect the double at about 59 mas and ΔM_bol < 1 mag.