Book covering introduction to mathematical proofs

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I am looking for some introductory books covering mathematical proofs, axioms, propositions, proof techniques etc in general.

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Check out "Mathematical Proofs: A Transition to Advanced Mathematics by Gary Chartrand, Albert Polimeni, and Ping Zhang". It is a great introduction to proof writing. The presentation is friendly and it contains lots of problems to work on. Another great book of this type is "Book of Proof by Richard Hammack". Check out this link to view the entire book http://www.people.vcu.edu/~rhammack/BookOfProof/. You could also check out "How to Prove it: A Structured Approach by Daniel Velleman", "Mathematical Reasoning: Writing and Proof by Ted Sundstrom", and "Proofs and Fundamentals: A First Course in Abstract Mathematics by Ethan Bloch. All of these books are worth checking out when learning the basics.