Katy Perry Sings 'Bad Blood' At Taylor Swift's Sydney Show, Old Feud Dead

Katy Perry's old feud with Taylor Swift is dunzo -- something we already knew, but which was double confirmed by the fact KP crashed her Aussie show ... and sang a certain song.

The pop star was one of a handful of famous people on hand Friday for T-Swift's first Sydney concert -- where she was hanging in the VIP tent with Rita Ora and, of course, Travis Kelce ... who flew on down to be with his girlfriend.

Katy's presence was interesting though ... on account that she and Tay Tay used to beef.

That's why her singing "Bad Blood" -- which has always been rumored to be about Katy -- was fascinating to see ... as Taylor belted out the tune onstage, she was being recorded singing along down in the crowd. It's the ultimate irony ... and proof they're all good now.

Katy even posted a picture with Taylor after the show ... and they look very chummy.

If you're unfamiliar ... the whole saga dates back to 2014 or so, when Taylor was first releasing "Bad Blood" -- during which she alluded to a rift in a friendship ... and most everyone assumed she was referring to Katy, explaining it was a personnel issue.

Taylor talked about it at the time without naming KP ... "She did something so horrible. I was like, ‘Oh, we’re just straight-up enemies.’ And it wasn’t even about a guy! It had to do with business. She basically tried to sabotage an entire arena tour."

TS added ... "She tried to hire a bunch of people out from under me. And I’m surprisingly non-confrontational – you would not believe how much I hate conflict. So now I have to avoid her. It’s awkward, and I don’t like it."

Katy ended up responding with her own diss track, of sorts, and went on to say that their feud was all about backup dancers -- namely, Katy hiring some of Taylor's own staffers.

In the end ... they ended up making up by the time Taylor dropped her song/video for 'You Need to Calm Down' -- in which Katy made a cameo ... and was clearly cool with her again.

Now, they're buddies, it seems, and all that bad blood has turned into water under a bridge.

Speaking of water ... there was a lot of it at Taylor's Sydney show -- albeit, well before curtain call. Some fans got caught in a brief downpour as they were filing into the stadium