BOSTON — Bank branches are not going anywhere.

That was the sentiment from three bank CEOs who spoke this morning at BAI’s Retail Delivery Conference here.

“Innovation is not a replacement” for traditional bank branches, said Richard Davis, CEO of U.S. Bancorp. “”You have to offer mobile banking and you have to have expensive bank branches.

“You have to be everything to everybody.”

Davis went as far as to recall a story from his days as a bank teller in 1985, when predictions were that bank branches would be obsolete by the turn of the century.

Mobile banking, iPhone apps, and other innovations should complement branches, or stores, as Bharat Masrani, CEO of TD Bank, calls them. “Every channel is important,” he said. “The new ways are not the only ways.”

Tellers everywhere just breathed a huge sigh of relief.