Is this proof for the non-differentiability of brownian motion rigorous enough?

[MathMan111]

I stumbled upon this video and I just wanted to know if this proof is rigorous enough.

YouTube Video: "Demonstrate the Non-differentiability of Brownian Path, starting with definition of derivative from ordinary calculus"

 

[mmm4444bot]

Video link has been fixed.

?

[imath]\;[/imath]