# Proof (mathematics)

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In mathematics, a **proof** of a statement
(called theorem, proposition, lemma, etc. according to the context and its importance)
is a series of arguments which show that the assumptions of the statement imply its conclusion.
Besides the assumptions listed explicitely in the statement to be proven,
the arguments — which have to be based on inference rules of mathematical logic —
may use the axioms of the theory and previously proven statements.