Informally, a procedure that brings conviction. More formally, a deductively valid argument starting from true premises, that yields the conclusion. Most formally, in proof theory, a proof is a sequence of formulae of which each member is either an axiom or is derived from a set of preceding members by application of a rule of inference, and which terminates with the proposition proved. The final member of such a sequence is a theorem . In 17th- and 18th-century usage ‘proof’ has the same implications of a chain of intuitive ideas as demonstration.
Philosophy dictionary. Academic. 2011.