Full Idea
The principle of Abstraction says that whenever a relation with instances is symmetrical and transitive, then the relation is not primitive, but is analyzable into sameness of relation to some other term. ..This is provable and states a common assumption.
Gist of Idea
The principle of Abstraction says a symmetrical, transitive relation analyses into an identity
Source
Bertrand Russell (The Principles of Mathematics [1903], §157)
Book Reference
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.166
A Reaction
At last I have found someone who explains the whole thing clearly! Bertrand Russell was wonderful. See other ideas on the subject from this text, for a proper understanding of abstraction by equivalence.