If @media all is declared in css then max-device-width is necessary?

If @media all is declared in css then max-device-width is necessary?

I am using media query @media all and (max-width:500px) {..} to make site
design responsive. It is working fine on my opera mini. But i have not
tested it on other other mobile browsers. Will it also work on other
mobile browsers or i have to add (max-device-width:500px) in this media
query.