Proof of Eberlein–Smulian Theorem for a reflexive Banach spaces Looking for the proof of Eberlein-Smulian Theorem. 
Searching for the proof is what I break with this morning. Some of my friends recommend Haim Brezis (Functional Analysis, Sobolev Spaces and Partial
Differential Equations). After I search the book, I only found the statement of the theorem, is the proof very difficult to grasp? Why is Haim Brezis skip it in his book?
Please I need a reference where I can find the proof in detail.


Theorem:(Eberlein-Smul'yan Theorem) A Banach space $E$ is reflexive if and
  only if every (norm) bounded sequence in $E$ has a subsequence which converges
  weakly to an element of $E$. 



Kôsaku Yosida, Functional Analysis, Springer 1980, Chapter V, Appendix, section 4. (This appears to be the 6th edition).
