theorem Th9: :: ANPROJ_1:9

for V being RealLinearSpace
for p, q, u, v being Element of V
for a1, b1, a2, b2 being Real st not are_Prop p,q & u = (a1 * p) + (b1 * q) & v = (a2 * p) + (b2 * q) & (a1 * b2) - (a2 * b1) = 0 & not p is zero & not q is zero & not are_Prop u,v & not u = 0. V holds
v = 0. V