Deleting emails from webmail server so as not to show again on smartphone later?

It's getting old having to delete every email twice from my inbox. I've dug around but can't find where I make the setting so when I delete while veiwing logged in my Verizon webmail on my laptop, I don't have to go thru and delete again from my iPhone an hour later when I check emails from there?

I don't want to be able permanently delete off the server from my phone, but I do want them taken offline once I've either read them or have read and deleted from the actual webmail site so they don't download again later on my phone. I pretty much have the phone set to not download emails until I manually open it.