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Yes, Chlorociboria aeruginosa aka Elfcups, is a perfect example.
But it is rather an exception to the general rule, right?

Elfcups - Chlorociboria aeruginosa by Christine Young.jpg

I hope I will encounter it one day, as well.

I only found it once hidden under some bark on a dead log. The only other blue mushroom I found was a blue turkeytail. I'm still looking for the indigo lactarius that theoretically might grow in my area. It has amazing blue gills.