let CLSP be CollSp; :: thesis: for a, b, c, d being Point of CLSP 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 Point of CLSP; :: thesis: ( a <> b & a,b,c are_collinear & a,b,d are_collinear implies a,c,d are_collinear )
assume A1: ( a <> b & a,b,c are_collinear & a,b,d are_collinear ) ; :: thesis: a,c,d are_collinear
a,b,a are_collinear by Th2;
hence a,c,d are_collinear by A1, Th3; :: thesis: verum