Cut through two perpendicular cylinders (intersecting faces)

[kloberemt]

I never have an issue intersecting different faces, but I am stuck. I have two cylinders that are the same diameter and are hollowed out. The intersect in a perpendicular fashion. The intent of the model is to make the tunnels, so I need to erase the crossing tube / cylinder. I cannot seem to get the faces to join so I can delete the crossing tube. Please help teach me the best way to accomplish this. Thanks in advance.

[Box]

It looks like the horizontal cylinder is in a different context to the edges.
Make sure you have the intersecting geometry in the same context, either as raw geometry or within the same group/component.