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

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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.

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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}## .
 
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