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The Shannon Briggs vs. Wladimir Klitschko feud just hit new levels -- with tensions exploding in a Florida gym ... and Evander Holyfield had to jump in to save the day ... TMZ Sports has learned.

Briggs -- a former heavyweight champ -- confronted his arch enemy in the boxing gym where they're both known to work out ... and as usual, got in Klitschko's face and called him out for refusing to fight him in the ring.

At one point, Wlad put one of his hands on Briggs -- which PISSED SHANNON OFF!

Things got physical and Briggs tells TMZ Sports .... that's when Holyfield, along with another boxing champ, Michael Moorer, jumped into action and separated the two.

By the way, the boxing champs are all in town to shoot a boxing documentary about heavyweights.