Troubleshooting a Derivation: Why μ*ε=1/c^2?

[snate]

I've been following the derivations in the following video up until that point. I don't quite understand why does it imply that μ*ε=1/c^2. Thanks.

 

[BvU]

Check out the wave equation earlier on in the video (10:20) . $v^2=\omega^2/k^2$ and ${1\over \mu_0\varepsilon_0}$ takes that place, so $v^2 = {1\over \mu_0\varepsilon_0}$ .