Finitely presented and residually finite implies solvable word problem

Statement
Any finitely presented residually finite group (i.e., a group that is both a finitely presented group and a residually finite group) is a group with solvable word problem.

Similar facts

 * Finitely presented and conjugacy-separable implies solvable conjugacy problem

Facts used

 * 1) uses::Finitely presented implies all homomorphisms to any finite group can be listed in finite time
 * 2) uses::Residually finite and all homomorphisms to any finite group can be listed in finite time implies solvable word problem

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