let AS be AffinSpace; :: thesis: ( AS is not AffinPlane implies AS is Desarguesian )
assume AS is not AffinPlane ; :: thesis: AS is Desarguesian
then for A, P, C being Subset of AS
for q, a, b, c, a', b', c' being Element of AS st q in A & q in P & q in C & q <> a & q <> b & q <> c & a in A & a' in A & b in P & b' in P & c in C & c' in C & A is being_line & P is being_line & C is being_line & A <> P & A <> C & a,b // a',b' & a,c // a',c' holds
b,c // b',c' by Th49;
hence AS is Desarguesian by AFF_2:def 4; :: thesis: verum