I think I also agree with you, and I agree with the fact that if Arsenal is able to beat Manchester City in their forthcoming match, that shouldn’t give them the feeling that they can win every other match that comes their way. Although the truth of the matter is, if Arsenal can win over Manchester City, it will be a huge relief for the club as a whole and increase their chances of winning the Champions League trophy. at the same time, if they start feeling that defeating one of their biggest contenders has given them the capacity to win all other matches, they may relax, which could lead to complacency and eventual failure.
Arsenal are strong, one of strongest clubs in Premier League this season so they are able to beat Manchester City. But Manchester City are strong too and they won 5 Premier League seasons in last six seasons, they are experienced enough to play against Arsenal. More important, there is another risk for Arsenal, Manchester City will host Arsenal at their home stadium and if Arsenal won't have proper careful approach for the big match, they will fall to a trap setup by Manchester City and risk to lose the match will be very high.
So, Arsenal needs to stay focused and put in as much effort in the upcoming matches as they did against Manchester City. They shouldn’t take any chances by relaxing or assuming that because they’ve beaten Manchester City, no other club can defeat them. That mindset will only lead to failure, and I agree with you.
They must fully focus at the match beginning and must avoid such thinking like they will be able to beat Manchester City easily. It will be Arsenal's suicide thinking for such a big match and if they lose this match, they will fall to a third position and see their chance to win Premier League becomes smaller a lot.