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SAN FRANCISCO (Reuters) - Pro Football Hall of Fame fullback Joe Perry, who was nicknamed "The Jet" for his electrifying speed on the gridiron, died on Monday at age 84.

Perry, the first NFL player to rush for 1,000 yards in consecutive seasons, died peacefully in Arizona early on Monday due to complications from dementia, according to his former team, the San Francisco 49ers.

"I was deeply saddened to hear of Joe Perry's passing earlier today," 49ers owner John York said in a statement. "A truly remarkable man both on and off the field, Joe had a lasting impact on the game of football and was an inspirational man to the generations of players that followed him."

Perry, who played 14 seasons for the 49ers (1948-1960, '63) and two for the Baltimore Colts (1961-62), rushed for 1,000 yards in the 1953 and 1954 seasons and remains San Francisco's all-time leader in rushing yards and rushing touchdowns.

Perry, who amassed a total of 9,723 rushing yards and was the NFL's all-time leading rusher until Jim Brown overtook him, was elected to the Pro Football Hall of Fame in 1969.

"All of us here at the Pro Football Hall of Fame are extremely saddened to learn of the passing of the great Joe Perry," Pro Football Hall of Fame President Steve Perry said in a statement.

"Joe was not only a key figure in the history of professional football, but he was a great friend to us here at the Pro Football Hall of Fame."

(Reporting by Julian Linden; Editing by Frank Pingue)