Smart mailboxes and Rules

I am trying to create a rule so that the massive amounts of political email I receive go into one folder no matter which email address receives them. I had created a smart mailbox to receive them but discovered that they were not removed from the original email boxes. I then tried to create a rule to make that happened; however, when I try to select the destination mailbox, the smart mailbox is not listed. What is another way to complete this task? Thanks.