It's really hard to answer this question when you phrase things so vaguely. I take your question to mean:
- There is a theorem, let's call it Theorem A.
- You thought you had three new results that are applications of Theorem A.
- You realized you could prove those results via a generalization of Theorem B instead.
If that's right, then from a mathematical-writing perspective, how about: "Three applications of (a generalization of) Theorem B"
I have certainly seen text like this in plenty of papers. Alternatively, you could ditch the language about "Applications of" and just focus your paper on the three examples, no matter how you prove whatever you are trying to prove about them.