hasitem={item=air} doesn't work proprly

I use /kill @a [hasitem={item=air}], but somehow it failed to kill my character even if i has empty slot on my inventory, i've tried to specify the requirements to address a specific slot, and it still didn’t work. This is so annoying because there is no other way to detect if a player is holding noting unless using this 'hasitem={item=air}' command.