let FdSp be FanodesSp; :: thesis: for a, b, c, d being Element of FdSp st a,b,c is_collinear & a,b,d is_collinear holds
a,b '||' c,d
let a, b, c, d be Element of FdSp; :: thesis: ( a,b,c is_collinear & a,b,d is_collinear implies a,b '||' c,d )
assume ( a,b,c is_collinear & a,b,d is_collinear ) ; :: thesis: a,b '||' c,d
then ( a,b '||' a,c & a,b '||' a,d ) by Def2;
hence a,b '||' c,d by PARSP_1:35; :: thesis: verum