I'm pretty sure that the advanced and professional use light bridge technology which allows a stronger signal requiring a cabled connection, so unfortunately I don't think the adapter would work if u have the p3 pro.
Actually, the lightning adapter may work if you have the p3 4k or standard because they use wifi video downlink instead of a lightning cable directly connecting to your phone.
Actually, I'm pretty sure the adapter will work with the p3 4k and standard becuase they use a wifi video downlink, so no cable to your ipad/iphone would be needed, allowing for the adapter to still function with its hdmi out to a separate device or tv