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In mathematics and logic, an axiomatic system or axiom system is a standard type of deductive logical structure, used also in theoretical computer science. It consists of a set of formal statements known as axioms that are used for the logical deduction of other statements. In mathematics these logical consequences of the axioms may be known as lemmas or theorems. A mathematical theory is an expression used to refer to an axiomatic system and all its derived theorems.
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