sigh of relief

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sigh of relief (plural sighs of relief)

1. A release of stress through breathing motions.
2. (idiomatic) A reassurance or support, something that reduces stress from an arduous activity.
   • 2005, Erich Hartung, America's Finest‎, page 149:

     Boyd was put in charge of SWAT three years later. Indeed, the force of the elite SWAT Team was a big sigh of relief for the other police offices on the ground. However, for the bank robbers, it was not.

• breathe a sigh of relief