If you have set up Imap mail accounts then all emails are saved on server and all imap account folders synchronise with server to show what is on the server. When you delete an email from laptop imap account it updates the server, so when you logon to PC imap account, it synchronises with server and shows exactly what is on server. So you are not going to see something that has been deleted by you. This is how all imap mail accounts work.