(Classic Outlook) automatically delete items in "Sent Folder" if sent to a specific person?

Hello all,

I've applied a rule to an inbox I'm using that automatically forwards all e-mail received there to my personal address.

Issue is, this clogs up the "sent" folder with pointless duplicates. 

So I tried to apply a rule to the "Sent" folder to get rid of these mails, issue is that once I select the rule "sent to user or public group" and write the e-mail address I want to filter, the options for the rule that appear afterwards don't include the "delete the e-mail" ones.

There's only the "create a copy and move to folder" option. Which is not what I need.

Any Idea on how I could solve this without contacting the mail server admin to auto forward from there?