How to punch a closed hole

 From:  Rich_Art
Hi All,

I making a bicycle lamp. I want to punch a closed hole trough the bottom of the body.
With boolean union it works. I just need to delete some parts.
When I want to join the different surfaces together so i can fillet the edges it will delete the top as well. (see image for better explanation)

How can I prevent this.

Rich_Art. ;-)

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