White started superbly, including a 130 break in the fourth frame to take a 3-1 lead, and looked ready to reach the final when set at the table in the next one, but a miss-hit swerve allowed Hendry to clear up to reduce the arrears to one.
The Whirlwind showed no nerves in the sixth frame though and takes his place in the final.
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Hendry won four World Championship finals against White at the Crucible - 1990, 1992, 1993 and 1994.
White will meet Ken Doherty in the final after the 1997 world champion beat fellow Dubliner Michael Judge 4-1 in the other semi-final.
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