Lambda Calculus - reduction with a shorthand term

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I'm new to lambda calculus and am having trouble understand how a shorthand acts when reducing.

Given: $((\lambda xy.x)(\lambda y.y))y$

What I have:

since $\lambda xy.x = \lambda x.\lambda y.x$

$((\lambda x.\lambda y.x)(\lambda y.y))y$

Now from here, I'm not sure how to continue with the reduction. I believe the whole thing is supposed to simplify to $xy$ but I'm not sure how to get there.