Testing for signficicance of the difference between two portfolio alphas

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Hello, I have the following problem:
I've run some regressions on attribute-sorted portfolios. Just a simple regression with the lm function (y = portfolio excess return, x = market index excess return)
I have two alphas, from portfolio 1 and portfolio 2. One is significant the other is not. So far so good.

Now I want to test whether the difference of the alphas is significant (alpha1 minus alpha 2)
I really don't know how to do that. Any help is appreciated!

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