Verb
breathe a sigh of relief (third-person singular simple present breathes a sigh of relief, present participle breathing a sigh of relief, simple past and past participle breathed a sigh of relief)
(idiomatic) to be relieved; to feel relief.
This programme to stop nuclear by 2020 is just crazy. If there were a nuclear war, and humanity were wiped out, the Earth would breathe a sigh of relief. James Lovelock