let V be RealLinearSpace; :: thesis: for u, w, v being VECTOR of V st {u,w,v} is linearly-independent & u <> v & u <> w & v <> w holds
{u,(- w),(- v)} is linearly-independent
let u, w, v be VECTOR of V; :: thesis: ( {u,w,v} is linearly-independent & u <> v & u <> w & v <> w implies {u,(- w),(- v)} is linearly-independent )
( - v = (- 1) * v & - w = (- 1) * w ) by RLVECT_1:29;
hence ( {u,w,v} is linearly-independent & u <> v & u <> w & v <> w implies {u,(- w),(- v)} is linearly-independent ) by Th31; :: thesis: verum