Finitely presented and conjugacy-separable implies solvable conjugacy problem

Statement
A finitely presented conjugacy-separable group (i.e., a finitely presented group that is also a  conjugacy-separable group) is a group with solvable conjugacy problem.

Similar facts

 * Finitely presented and residually finite implies solvable word problem

Facts used

 * 1) uses::Finitely presented implies all homomorphisms to any finite group can be listed in finite time
 * 2) uses::Conjugacy-separable and all homomorphisms to any finite group can be listed in finite time implies solvable conjugacy problem

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