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The Blues sealed their place in the last four with a dominant performance at the Riverside Stadium.
David Silva opened the scoring in the third minute before Sergio Aguero sealed progression into the semi-final in the 67th minute.
City controlled possession in the North East with Claudio Bravo responding when called upon on few occasions.
Pep Guardiola's side will now face one of Arsenal/Lincoln City, Spurs/Millwall or Chelsea/Manchester United at Wembley Stadium in the semi-final with the draw set to take place on Monday evening.