Also registering wins on Monday afternoon were Joe Perry, Mark King, Robert Milkins and Ali Carter.
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Sambora and Bon Jovi are no Keith Richards and Mick Jagger or Steven Tyler and Joe Perry.
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Aerosmith's Steven Tyler and Joe Perry are among the latest inductees into the Songwriters Hall of Fame.
Carter looked jaded after a gruelling fortnight which saw him edge past Joe Perry in a marathon semi-final.
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Doherty will now take on Joe Perry in the last 16 on Monday.
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Carter faces Joe Perry after a 4-0 win over Irishman Fergal O'Brien.
Australia's Neil Robertson beat Ireland's Fergal O'Brien 5-2, world number five John Higgins beat Tom Ford 5-4 and Joe Perry beat Matthew Stevens 5-1.
Doherty opened a 5-3 advantage over Joe Perry in their first session, while Ding led by the same scoreline against 2003 champion Matthew Stevens.
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In a repeat of their first round match at this year's World Championships, Joe Perry had been hoping for revenge on Jamie Cope after losing 10-6 in Sheffield.
In other matches John Parrott bowed out at the first hurdle after a 5-2 loss to Cambridgeshire cueman Joe Perry, who will now meet last season's UK champion Peter Ebdon.
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Earlier, defending champion Neil Robertson crashed out after a 4-2 defeat in his final group match against Stephen Lee, Joe Perry beat Joe Swail 4-2 to finish runner-up in their group.
Robertson needs a win, while a draw will be good enough for Doherty, with the victor set to play either world champion John Higgins or Joe Perry , the only players who can now qualify from Group one.
The hosts led 17-8 at the break thanks to two Joe Maddock tries, with Bristol's try coming when Lee Robinson gathered a Shaun Perry chip ahead.
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