Best proof of some theorems in calculus

Question

I would like to choose (among the miriads of proofs) a well-structured, elegant, neat, clear proof of

• the first fundamental theorem of calculus;

• the second fundamental theorem of calculus;

• the mean value theorem;

• the intermediate value theorem;

• Weierstrass theorem;

• Rolles' theorem.

Which book (I can choose among Spivak, Stewart, Apostol and a few other ones) offers the well-structured, elegant, neat, clear proof of them (NB you can pick a different book for every theorem if it is the case)?

Added: Do you think that Apostol's proofs are elegant and rigorous?

Answer 1

In my humble opinion, Rudin's "Principles of Mathematical Analysis" is what you are seeking.