Is there a general book of mathematics which starts from first order logic, treats set theory (in ZF setting) in which first order logic is used, then abstract algebra (in which set theory is heavily used), topology (at least point set topology) and finally mathematical analysis (in which all the previous concepts are used). In all these parts most important results should be covered.
In this way one can study mathematical analysis having solid foundations of mathematics? Am I dreaming or a book of this kind exists?