Resources from Trade

[MenacingVitamin]

I'm confused a little about this. In the city menus (of cities connected to the network), in the resource box, the little icons that represent iron, copper, etc. all say they give a +1 hammer each. It doesn't seem like they give the bonus to the city's production though. Am I missing something here?

 

[MenacingVitamin]

I may have explained this badly, so I am including a visual. The stone resource in this screenshot indicates that +1 to production is granted, but the city's production does not register this. It's confusing to me, because (in the resource box), the luxuries and food resources give noticable health and happiness, but the strategic resources do not add the production to the city as it would seem they would. Anyone have a good explanation?