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Cape Town - Following a crucial Michael Dawson winner against Liverpool, the Hull City Tigers are now 15th in the Premier League table, four points above the drop zone having played a game more than Sunderland and Leicester City.
Hull have some tough fixtures in their final sprint, with Tottenham and Manchester United amongst their final four matches, along with fellow relegation contenders Burnley.
Before that they have to take on Arsene Wenger's team, who had won their last eight in a row prior to their goalless draw with Chelsea last weekend.
But after overcoming the Reds, Bruce is bullish about his side's chances at home against the Gunners next Monday.
"I've never really doubted the character. We've had a lot to put up with, with injuries and conceding in the last minute - we've lost 10 points, especially before Christmas in that situation.
"The one thing I've come to know is the vast majority of them (the players) are desperate to be in the Premier League and I think that's showed in the last couple of performances.
"We've got to produce another few performances and another couple of good results. It's difficult against Arsenal but we went to the Emirates and got a result down there so if we are capable of doing that then we've got a chance at our place.
"We give ourselves a good chance, but we still need a couple of results. I don't think 34 [points] is enough history tells us that. We're all delighted, but back to work in the morning.
"Commitment is the secret to winning against the big teams. We've set a benchmark and Arsenal won't fancy coming here now."
