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Frida Maanum’s Arsenal, who beat Aston Villa 4-0 in the second semi-final, await in the final.
It took just eight minutes for Lauren James to put Chelsea ahead after being played in by Mayra Ramirez.
The joy was short-lived for Colombian Ramirez, who was replaced with an injury barely half an hour later.
Chelsea could still let loose the cheers for a 1-0 victory and a ticket to the final when the referee blew the match off.
Guro Reiten started for the London team and was replaced after 64 minutes. Maren Mjelde was not in Thursday’s match due to injury problems.
The final will be played on 31 March at Molineux in Wolverhampton.
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