[en] An isotope of the 113th element, i.e., ²⁷⁸113, was produced in a nuclear reaction with a ⁷⁰Zn beam on a ²⁰⁹Bi target. We observed six consecutive α-decays following the implantation of a heavy particle in nearly the same position in the semiconductor detector under an extremely low background condition. The fifth and sixth decays are fully consistent with the sequential decays of ²⁶²Db and ²⁵⁸Lr in both decay energies and decay times. This indicates that the present decay chain consisted of ²⁷⁸113, ²⁷⁴Rg (Z=111), ²⁷⁰Mt (Z=109), ²⁶⁶Bh (Z=107), ²⁶²Db (Z=105), and ²⁵⁸Lr (Z=103) with firm connections. This result, together with previously reported results from 2004 and 2007, conclusively leads to the unambiguous production and identification of the isotope ²⁷⁸113 of the 113th element. (author)