let FdSp be FanodesSp; :: thesis: for a, b, c, d being Element of FdSp st a,b,c are_collinear & a,c,d are_collinear & a <> c holds
b,c,d are_collinear
let a, b, c, d be Element of FdSp; :: thesis: ( a,b,c are_collinear & a,c,d are_collinear & a <> c implies b,c,d are_collinear )
assume that
A1: a,b,c are_collinear and
A2: ( a,c,d are_collinear & a <> c ) ; :: thesis: b,c,d are_collinear
A3: a,c,c are_collinear by Th12;
a,c,b are_collinear by A1, Th10;
hence b,c,d are_collinear by A2, A3, Th13; :: thesis: verum