Mail in smart mailboxes also shows up in inbox

Maybe I'm misunderstanding the purpose of smart mailboxes. I have a number of them that work as they are supposed to, and sort incoming mail into the right spot. So I go to smart mailbox 'creditcards' and there they are, BUT they still show up in the (very overcrowded) inbox, where I do not want to see them.

If I delete mail from the inbox, it disappears from the smart mailbox, too.

What I am imagining: I think of Apple Mail as a file cabinet where all incoming mail shows up. Somebody behind the scenes sorts through the incoming mail and moves the credit card statements to a folder in another drawer. Exactly as it should be.

But the way it's working is the the person behind the scenes finds the credit card statements, copies them, leaves the originals in the big file and puts the copies in the separate folder in a separate drawer.

Is there a way to make this work?