let CLSP be CollSp; :: thesis: for a, b, c, d being Point of CLSP st a <> b & a,b,c is_collinear & a,b,d is_collinear holds
a,c,d is_collinear
let a, b, c, d be Point of CLSP; :: thesis: ( a <> b & a,b,c is_collinear & a,b,d is_collinear implies a,c,d is_collinear )
assume A1: ( a <> b & a,b,c is_collinear & a,b,d is_collinear ) ; :: thesis: a,c,d is_collinear
a,b,a is_collinear by Th7;
hence a,c,d is_collinear by A1, Th8; :: thesis: verum