A formal proof is a rigorous mathematical demonstration that establishes the truth of a statement or theorem through a series of logical deductions based on agreed-upon axioms and inference rules. Formal proofs are characterized by their strict adherence to a defined formal system, which includes: 1. **Axioms**: Fundamental statements or propositions assumed to be true without proof. They serve as the starting point for any arguments or proofs.
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A proof in some system for the formalization of mathematics.