A formal series of statements showing that if one thing is true something else necessarily follows from it WordNet 3.0 & Open English WordNet

In logic and mathematics, a formal proof or derivation is a finite sequence of sentences, each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference. Wikipedia

A fully rigorous proof as is possible only in a formal system Wikipedia Disambiguation

A construct in proof theory Wikipedia Disambiguation

A sequence of statements consisting of axioms, assumptions, statements already demonstrated in another proof, and statements that logically follow from previous statements in the sequence, and which concludes with a statement that is the object of the proof. Wiktionary