Can Wedderburn's theorem proof be given by integral domain argument directly?

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Wedderburn's theorem states as every finite division ring is field And we know that every Finite integral domain is field. So why not we are using that fact to prove that theorem? As every division ring is integral domain.

I don't know any shortfall in my question but this question came just in my mind And I can not have any argument against it. That's why I was asking Please help me out