(Solved): In 1889 , Giuseppe Peano introduced the following two axioms: P1. If A,B, and C are three non-coll ...

In 1889 , Giuseppe Peano introduced the following two axioms: P1. If $$A,B$$, and $$C$$ are three non-collinear points, $$D$$ and $$E$$ are such that $$A?B?D$$ and $$A?E?C$$, the there is a point $$F$$ such that $$E?F?D$$ and $$B?F?C$$. and P2 If $$A,B$$, and $$C$$ are three non-collinear points, $$D$$ and $$E$$ are such that $$A?B?D$$ and $$B?C?E$$, the there is a point $$F$$ such that $$D?E?F$$ and $$A?F?C$$. It is easy to show that I1-I3, B1-B4 imply P1 and P2. Is is true that I1-I3, B1-B3, P1, P2 imply B4? If yes, provide a proof, if no, a counterexample (an independence model).