The convincing win already puts Barcelona two points clear of Real Madrid, who drew with Valencia.
“It has been a difficult time and it is nice to be back,” Villa told Spanish television.
“I am pleased to be able to say I can forget about the injury now. I have had five weeks training at the maximum level but my body still struggles to reach the levels necessary to play more minutes.
“I’ll keep on working until I can eventually play a full game again.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.