let AS be AffinSpace; ( AS is not AffinPlane implies AS is translational )
assume
AS is not AffinPlane
; AS is translational
then
for A, P, C being Subset of AS
for a, b, c, a9, b9, c9 being Element of AS st A // P & A // C & a in A & a9 in A & b in P & b9 in P & c in C & c9 in C & A is being_line & P is being_line & C is being_line & A <> P & A <> C & a,b // a9,b9 & a,c // a9,c9 holds
b,c // b9,c9
by Th51;
hence
AS is translational
by AFF_2:def 11; verum