let FdSp be FanodesSp; :: thesis: for a, b, c, d being Element of FdSp st parallelogram a,b,c,d holds
parallelogram b,a,d,c
let a, b, c, d be Element of FdSp; :: thesis: ( parallelogram a,b,c,d implies parallelogram b,a,d,c )
assume A1: parallelogram a,b,c,d ; :: thesis: parallelogram b,a,d,c
then a,b '||' c,d by Def3;
then A2: b,a '||' d,c by PARSP_1:23;
a,c '||' b,d by A1, Def3;
then A3: b,d '||' a,c by PARSP_1:23;
not b,a,d is_collinear by A1, Th36;
hence parallelogram b,a,d,c by A2, A3, Def3; :: thesis: verum