I'm a first-year math student and have studied single-variable calculus for quite some time. However, with so many proofs and theorems, it's easy to get lost and forget how everything links together (I want to quickly see how I can link bank any theorem to fundamental concepts and axioms I began with). For this reason, I need not so much a calculus textbook like Spivak's but rather a reference collection of calculus theorems and proofs compiled and ordered in one place. Basically a book which starts from basic properties of real numbers and notions like epsilon-delta proofs and works its way up through calculus without any explanations, examples or exercises.
It sounds like you basically want an introductory real analysis textbook, like Rudin's Principles of Mathematical Analysis. If you want less examples, look to something by Kolmogorov or someone Russian. And you can ignore the exercises as well even if they're there.