Axioms work as...

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Explanation

Axioms are accepted without proof within the system, and results are derived from them. Conclusions are proved, not assumed at the start.

An axiomatic system is a triple \(\mathcal{S}=(\mathcal{L},\mathcal{A},\mathcal{R})\) made of a formal language, axioms and rules of inference.

\[\mathcal{S}=(\mathcal{L},\mathcal{A},\mathcal{R})\]