let PCPP be CollProjectiveSpace; :: thesis: for p, q being Element of PCPP st p <> q holds
ex r being Element of PCPP st not p,q,r are_collinear
let p, q be Element of PCPP; :: thesis: ( p <> q implies ex r being Element of PCPP st not p,q,r are_collinear )
consider a, b, c being Element of PCPP such that
A1: not a,b,c are_collinear by COLLSP:def 6;
assume p <> q ; :: thesis: not for r being Element of PCPP holds p,q,r are_collinear
then ( p,q,a are_collinear & p,q,b are_collinear implies not p,q,c are_collinear ) by A1, ANPROJ_2:def 8;
hence not for r being Element of PCPP holds p,q,r are_collinear ; :: thesis: verum