Can Newton's Laws of Motion be simplified?

Newton's first law that an object not acted upon by a force maintains a uniform velocity is really a special case of his second law F = ma, in the special case that F= 0.

So there really are only two independent Newton's Laws.
 Andrew Mason: I don't like your derivation of the third law from Galilean relativity. Suppose that we have a system of three particles A,B,C. Then the condition that the momentum is conserved in the system is as you say: (Fab+Fac+Fba+Fbc+Fca+Fcb)*dt=0 But I don't see how setting Fxy = -Fyx is the only solution to that equation. How about for instance: Fac = -Fab, Fba=-Fbc,Fca=-Fcb? why couldn't I assume that. It would be a wicked world yes, but I don't see a problem with it.

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