let FdSp be FanodesSp; :: thesis: for a, b, c, d being Element of FdSp st a,b congr c,d & not a,b,c is_collinear holds
parallelogram a,b,c,d
let a, b, c, d be Element of FdSp; :: thesis: ( a,b congr c,d & not a,b,c is_collinear implies parallelogram a,b,c,d )
assume that
A1: a,b congr c,d and
A2: not a,b,c is_collinear ; :: thesis: parallelogram a,b,c,d
( a,b '||' c,d & a,c '||' b,d ) by A1, Th58, Th59;
hence parallelogram a,b,c,d by A2, Def3; :: thesis: verum