# Newton's first law of motion a corollary of second law? [duplicate]

His first law of motion states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force.

That means, delta(a) = 0 if external F = 0. ..... (i)

His second law of motion can be formally stated as follows: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

That means, delta(a) = F/m. ...... (ii)

If we put F = 0 in eq. (ii), then we get delta(a) = 0. But wait! Isn't this exactly what first law says? So is first of law a corollary of the second law? And if so, why the obviously-not-stupid Newton proposed it as another law rather than proposing a corollary? Are we missing something?