theorem Th28: :: RLVECT_4:28

for a, b being Real
for V being RealLinearSpace
for u, v, w being VECTOR of V st {u,w,v} is linearly-independent & u <> v & u <> w & v <> w & a <> 0 & b <> 0 holds
{u,(a * w),(b * v)} is linearly-independent