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Dempster, 35, has gone 5-5 with a 2.25 ERA in 16 games/starts for the Cubs this season. His 1.038 WHIP this season ranks 6th in the majors and 3rd in the National League.
This is the second deal with the Cubs today, after the Rangers acquired backup catcher Geovany Soto from Chicago this morning.
The Rangers will hold a press conference to discuss today's transactions at 4 p.m. CT. Watch it live on texasrangers.com.