Don't panick but watch Brodie very close for a few days just in case.

My Rosco also takes prednisone every 3rd day.(We switched to prednisolone)
It's almost the same.

I'm sure Brodie will pass it fine.My Sam eats everything in site too.He scares me so very much.He's the type if you dropped a glass he'd probably run and eat it.I have no idea why he doesn't sniff it first.He's just like a dog.Wags his tail when he's happy too.Total dog personality.
Sam (The dog kitty) is in the very front the first white kitty you see.He doesn't look like dog does he