Mathematical analysis book with Lambda calculus notation.

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I am searching for a book in which we can find the theorems and definition written using $\forall \epsilon, \exists \delta $ types of notation only. when I am wringing proves it is very easy to follow them when I write down the problem in $\forall \epsilon, \exists \delta $ form.

The notation I am talking about is used in lambda calculus. I am not very familiar with Lambda calculus. The logic is very clear when I read things written explicitly in the form of Lambda calculus notation.

I am a 3-year undergraduate. suggest some Mathematical analysis book.