let PCPP be CollProjectiveSpace; for a, b, c, d being Element of PCPP st a <> b & a,b,c are_collinear & a,b,d are_collinear holds
a,c,d are_collinear
let a, b, c, d be Element of PCPP; ( a <> b & a,b,c are_collinear & a,b,d are_collinear implies a,c,d are_collinear )
A1:
a,b,a are_collinear
by ANPROJ_2:def 7;
assume
( a <> b & a,b,c are_collinear & a,b,d are_collinear )
; a,c,d are_collinear
hence
a,c,d are_collinear
by A1, ANPROJ_2:def 8; verum