I don't know why you are getting downvoted. I haven't had my morning coffee yet, so I am cynically going to presume a bunch of folks think you're nitpicking on

I don't know why you are getting downvoted. I haven't had my morning coffee yet, so I am cynically going to presume a bunch of folks think you're nitpicking on the words, but you're not. The derivation is correct, but it is not a proof of anything. Maxwell's equations aren't textbook PDEs that exist in a vacuum, devoid of any connection with the surrounding world. They are quantitative approximations of real-life phenomenae, that hold only under very specific circumstances, and break when those conditions (about e.g. distances) aren't met. The proof that the speed of light in vacuum (which the article "helpfully" fails to mention) is constant is experimental. If the experiment would fail, Maxwell's equations would have to be modified. Any predictions they make are tested against the reality, not vice-versa. Oh yes: I'm not nitpicking about their failure to mention it's the speed of light in vacuum. The final expression is constant only because \mu and \varepsilon are (supposed to be) constant in vacuum. Precisely the same expression predicts the (correct!) fact that the speed of light is not constant, but depends on the properties of the material it is travelling through. Edit: this should be very obvious from the fact that the derivation is based entirely on the four laws that constitute Maxwell's equations, not on theorems. Laws are not deduced mathematically, but formulated by experiment. Their predictions cannot constitute a proof. It may be tempting to treat their predictions as such, because in mathematics any correct result obtained by derivation can constitute a proof, but this is not the way to look at a set of physical laws. Maxwell's equations also "prove" that things like squeezed light cannot exist -- despite the fact that it clearly does, since we can generate it. These incorrect predictions are not onthologically different from correct ones.