Full Idea
The [Axiom of Choice] is also equivalent to the assumption that of any two cardinals which are not equal, one must be the greater.
Gist of Idea
Choice shows that if any two cardinals are not equal, one must be the greater
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], XII)
Book Reference
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.124
A Reaction
It is illuminating for the uninitiated to learn that this result can't be taken for granted (with infinite cardinals).