let FdSp be FanodesSp; :: thesis: for a, b, c, d being Element of FdSp st a,b,c is_collinear & a,c,d is_collinear & a <> c holds
b,c,d is_collinear
let a, b, c, d be Element of FdSp; :: thesis: ( a,b,c is_collinear & a,c,d is_collinear & a <> c implies b,c,d is_collinear )
assume ( a,b,c is_collinear & a,c,d is_collinear & a <> c ) ; :: thesis: b,c,d is_collinear
then ( a <> c & a,c,b is_collinear & a,c,c is_collinear & a,c,d is_collinear ) by Th15, Th18;
hence b,c,d is_collinear by Th19; :: thesis: verum