Finitely generated and free implies Hopfian

Statement
Any finitely generated free group is Hopfian: it is not isomorphic to any proper quotient of itself.

Related facts

 * Retract of free group is free on fewer generators
 * Free quotient group admits a section

Facts used

 * 1) uses::Free implies residually finite
 * 2) uses::Finitely generated and residually finite implies Hopfian

Proof
The proof follows directly by combining facts (1) and (2).