theorem Th9: :: ANPROJ_2:9

for V being RealLinearSpace
for o, u, v, w, u1, v1, w1, u2, v2, w2 being Element of V st not o is zero & u,v,w are_Prop_Vect & u2,v2,w2 are_Prop_Vect & u1,v1,w1 are_Prop_Vect & o,u,v,w,u2,v2,w2 lie_on_an_angle & o,u,v,w,u2,v2,w2 are_half_mutually_not_Prop & u,v2,w1 are_LinDep & u2,v,w1 are_LinDep & u,w2,v1 are_LinDep & w,u2,v1 are_LinDep & v,w2,u1 are_LinDep & w,v2,u1 are_LinDep holds
u1,v1,w1 are_LinDep