theorem Th23: :: ANPROJ_2:23

for V being non trivial RealLinearSpace
for p, q, r being Element of (ProjectiveSpace V) holds
( p,q,r are_collinear iff ex u, v, w being Element of V st
( p = Dir u & q = Dir v & r = Dir w & not u is zero & not v is zero & not w is zero & u,v,w are_LinDep ) ) by ANPROJ_1:24, ANPROJ_1:25;