A stability criterion

We come up with an independent proof for a corollary to the main theorem in [Yu. L. Ershov, “Stability preservation theorems”, Algebra Logika, 47, No. 3, 269–287 (2008)], since that corollary is the degenerate case of the main theorem (with empty sets $B_0$ and $B_1$), which establishes a stability criterion for a Henselian valued field. Such a proof is given here based on an analysis of tame and purely wild extensions made in [Yu. L. Ershov, “Tame and purely wild extensions of valued fields”, Algebra Analysis, 19, No. 5, 124–136 (2007)].