What are some recommended books for elementary math proofs?

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I just started reading the introductory section of Spivak's calculus, and it has an introduction about the main mathematical properties; dristributive, associative etc. also how basic operations such as multiplication arises naturally from addition and division from multiplication.

What caught my attention was a proof about 1 being greater than 0. due to the fact that
n square has to be greater than 0. and since 1 square = 1, then 1 is greater than 0.

Right now I am reading Spivak and Apostol's introduction to basic math but I was wondering if there are books that deal with this kind of elementary proofs, can someone recommend me some?

I don't mean books about logic but about elementary math like the above mentioned. I am having a hard time finding any book about this subject.
 
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How to Read and Do Proofs by D. Solow

of course this is at a much more elementary level than Spivak.