A finite basis for the identities of the Lie algebra \({\mathfrak sl}_ 2(K)\) over a field K of characteristic 0 was found by Yu. P. Razmyslov [Algebra Logika 12, 83-113 (1973; Zbl 0282.17003)] and V. T. Filippov [Algebra Logika 20, 300-314 (1981; Zbl 0496.17012)] established that all identities follow from the identity \[ [y,z,[t,x],x]+[y,x,[z,x],t]=0. \] In the present paper the author proves that Filippov’s theorem can be extended to the case of an arbitrary infinite field K. Since the technique of the Young diagrams is not valid in this case the author has improved it using some results of C. De Concini and C. Procesi [Adv. Math. 21, 330-354 (1976; Zbl 0347.20025)].