consider F being strict Field;
for x, y being Scalar of F holds
( not x * y = 0. F or x = 0. F or y = 0. F ) by VECTSP_1:44;
then F is domRing-like by Def5;
hence ex b₁ being comRing st
( b₁ is strict & not b₁ is degenerated & b₁ is domRing-like ) ; :: thesis: verum