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 that
A1: a,b,c is_collinear and
A2: ( a,c,d is_collinear & a <> c ) ; :: thesis: b,c,d is_collinear
A3: a,c,c is_collinear by Th18;
a,c,b is_collinear by A1, Th15;
hence b,c,d is_collinear by A2, A3, Th19; :: thesis: verum