let SAS be Semi_Affine_Space; for a, b, o being Element of SAS holds a,b // opposite a,o, opposite b,o
let a, b, o be Element of SAS; a,b // opposite a,o, opposite b,o
sum b,(opposite b,o),o = o
by Def6;
then
congr o,b, opposite b,o,o
by Def5;
then A1:
congr b,o,o, opposite b,o
by Th89;
sum a,(opposite a,o),o = o
by Def6;
then
congr o,a, opposite a,o,o
by Def5;
then
congr a,o,o, opposite a,o
by Th89;
hence
a,b // opposite a,o, opposite b,o
by A1, Th93; verum