Full Idea
A 'theorem' is defined as the last line of a proof in which each line is either an axiom or follows from earlier lines by a rule.
Gist of Idea
A 'theorem' is an axiom, or the last line of a legitimate proof
Source
Theodore Sider (Logic for Philosophy [2010], 9.7)
Book Reference
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.250
A Reaction
In other words, theorems are the axioms and their implications.