let FdSp be FanodesSp; :: thesis: for a, b, c, d being Element of FdSp st parallelogram a,b,c,d holds
parallelogram a,c,b,d
let a, b, c, d be Element of FdSp; :: thesis: ( parallelogram a,b,c,d implies parallelogram a,c,b,d )
assume A1: parallelogram a,b,c,d ; :: thesis: parallelogram a,c,b,d
then A2: a,c '||' b,d by Def3;
( not a,c,b is_collinear & a,b '||' c,d ) by A1, Def3, Th36;
hence parallelogram a,c,b,d by A2, Def3; :: thesis: verum