When a customer clicks the 'add to cart' button on tpl_product_info_display.php .... is there a way to then turn off the button so it's no longer visible?

I have a message which displays 'Successfully added item to cart!', but some people still seem to miss this and click the 'add to cart' button a second time just to make sure. Would be great if I could stop this by adding a bit of code which removes it but I don't have the knowledge to do this.