let FCPS be up-3-dimensional CollProjectiveSpace; :: thesis: for p being Element of FCPS holds
not for q, r being Element of FCPS holds p,q,r are_collinear
let p be Element of FCPS; :: thesis: not for q, r being Element of FCPS holds p,q,r are_collinear
consider q being Element of FCPS such that
A1: p <> q and
p <> q and
p,p,q are_collinear by ANPROJ_2:def 10;
not for r being Element of FCPS holds p,q,r are_collinear by A1, COLLSP:12;
hence not for q, r being Element of FCPS holds p,q,r are_collinear ; :: thesis: verum