I have 3 fields defined in my XML file like so:
You can chain the attribute values of showon, using [AND], like so:
Adding more fields to the chain is also allowed.
On a side note, you can use an [OR] clause in the chain too, adding more complexity, for example:
Update for Joomla 3.7:
As of Joomla 3.7, you will be able to to use the ! operator (not equal to):
This means, if field1 does not equal 1