This is misleading. The first law isn't a special case of the second and to think of it that way ignores the logic of why we say there are three laws in the first place.

The second law, F = ma, is only valid in so-called "inertial" reference frames. What is an inertial reference frame? Well... If you just started with the second law, you're stuck. It doesn't say anything about what an inertial reference frame is.

The first law is what establishes this, and this is why it is stated before the second law. The first law defines inertial reference frames as frames where you the following properties are true: * Objects observed with no forces acting on them, which are at rest, stay at rest * Objects observed with no forces acting on them, which are moving at some constant speed, stay in motion with the same speed and direction

I know this is nitpicky, but technically the second law is useless unless you know in what kinds of coordinates it is valid in. If I measure forces and accelerations while spinning around on a merry-go-round, then F will not be equal to the mass times the acceleration, in that rotating frame. Of course, by the first law, we can tell that the merry-go-round reference frame isn't inertial.

I point this out because I think it makes the logic of why on Earth we talk about there being three, not two, laws of motion actually make sense, as opposed to being for some weird historical reason.