Mickelson hasn't missed a Ryder Cup squad since the early 1990s having played in a record 11 consecutive tournaments.
USA captain Jim Furyk had an easy time with three of his four picks.
The matches are September 28-30 outside Paris.
When Mickelson, 48, won in Mexico in the March to end a five-year winless drought, he thought it would be a certainty he'd be on the team. It will be his eighth Ryder Cup (he is 13-17-3 overall).
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Team captains Maurkice Pouncey and Cam Heyward said they've communicated with Bell, but they wouldn't disclose particulars. Bell has stayed away from the team as a way to avoid injury and exercise his leverage as he seeks a contract extension.
The US captain will announce his final place on the defending champions' team next week, with Tony Finau regarded as the front-runner for the position.
DeChambeau, who attended the 2016 Ryder Cup at Hazeltine as a fan, said after his win at Ridgewood that playing he'd been on a "mission" to make the Ryder Cup team.
Mickelson said ending that long USA wait for a victory in Europe was his prime motivation.
"I've been trying to get that week in and week out and I was able to figure something out last week on the putting green and that's kind of progressed me to move forward in the right way". "It's been a really good year, and although I fell just shy of making it on points, it feels great to be a part of this team and serve this team in any way I can". Furyk will make his fourth captain's choice selection at the conclusion of the BMW Championship, which is being held this week at Arnonimink Golf Club in Newtown Square. "But it could have been a lot more hard".
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It's also a shame for other reasons as well, mainly the return the Blue Jays received from Cleveland, or lack thereof. The 32-year-old Donaldson was the league's top player in 2015, when he batted.297 with 41 homers and 123 RBIs.
DeChambeau, 24, had virtually guaranteed himself one of the captain's picks after storming to victory in the opening two legs of the PGA Tour's FedEx Cup playoff series, winning the Northern Trust and Dell Technologies Championship.
It was the third win of the year for DeChambeau, who also won the playoff opener at Ridgewood and is guaranteed the No. 1 seed for the Tour Championship regardless of what happens in the third round.
"I wouldn't have written it any better, to be honest with you", DeChambeau said. "And it showed, and it paid off". "It's a well-rounded team, and we'll go to work, get set to go".
"It's incredible to look back at the start of the year and now to have accomplished a goal like this to be a part of this team as a player is beyond special, " Woods said. 9, 10 and 11 in points when qualifying ended for eight automatic berths after the PGA Championship. The event is the one being removed as the FedEx Cup playoffs are shortened from four events to three.
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To find out if you're eligible for a fix , you can visit Apple's support post on the issue and enter your iPhone's serial number. Don't be surprised if Apple removes the headphone jack from the new iPads which which offer better battery life and performance.
European captain Thomas Bjorn announces his wild-card selections on Wednesday, with Henrik Stenson, Ian Poulter and Paul Casey among the likely picks.