let PCPP be CollProjectiveSpace; :: thesis: 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; :: thesis: ( 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 ) ; :: thesis: a,c,d are_collinear
hence a,c,d are_collinear by A1, ANPROJ_2:def 8; :: thesis: verum