Hidden Body Parts

I have one, you have one.
If you remove the first letter, a bit remains.
If you remove the second, bit still remains.
After much trying, you might be able to remove the third one also, but it remains.
It dies hard!

(Scoll Down for Solution)

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Solution

1. head
2. toe
3. arm
4. hand
5. nose
6. knee
7. mouth
8. finger