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The Catalans shrugged off their surprise loss to Rubin Kazan in the Champions League midweek and produced a dominant display helped by a Seydou Keita hat trick and two goals from Zlatan Ibrahimovic.
Barca are now on 22 points, three ahead of Real Madrid, who failed to bounce back from their midweek loss to AC Milan by drawing with Sporting Gijon 0-0 on Saturday. Sevilla are third on 16 points.
"We have proved that Barcelona is a big team,'' said Keita after the game.
"I'm happy but I am not a goal scorer. If (Leo) Messi or Ibrahimovic scores, it's better for the team.''