Full Idea
'Theorem': given a derivation of the sentence φ from the axioms of the theory T using the background logical proof system, we will say that φ is a 'theorem' of the theory. Standard abbreviation is T |- φ.
Gist of Idea
A 'theorem' of a theory is a sentence derived from the axioms using the proof system
Source
Peter Smith (Intro to Gödel's Theorems [2007], 03.4)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.23