I've slipped, and I can't get up!

[EngLearner]

There's this phrase I found here:

I've fallen, and I can't get up!

I wonder if the following version with the word "slipped" also makes sense:

I've slipped, and I can't get up!

Can the present perfect "I've slipped" be used to mean that "I'm now on the floor"?

 

[emsr2d2]

Using "slipped" alone doesn't suggest that you're on the floor. It's "I can't get up" that tells us you're on the floor. If I said "I slipped", I would normally mean that I briefly lost my footing but probably recovered it and stayed on my feet. If I used "I slipped over", that would mean that I ended up on the floor.
I would add "over" after "fallen" in the original sentence (in BrE) although "fallen" on its own is grammatically correct.