Filter Multiple Catergories

I have create a custom post which uses multiple catergories as highlighted below:
* Los Angeles
* San Francisco
* Painter
* Plumber

With use of taxonomies I can create a page that bring back all posts which have the Los Angeles catergory ticked and also a seperate one which shows Painter.

Is it possible a search query can be made to show me page which any posts which have both Los Angeles and Painters (i.e. Los Angeles Plumber wouldn’t show, even though he matches the LA box he doesnt match both). So I can tell give people a page that shows them all the Painters in Los Angeles.