Full Idea
We can show (using the axiom of choice) that the less-than relation, <, well-orders the ordinals, ...and that it partially orders the ordinals, ...and that it totally orders the ordinals.
Gist of Idea
The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers
Source
William D. Hart (The Evolution of Logic [2010], 1)
Book Reference
Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.26