30% cdr after selling Ionian Boots of Lucidity even though I had Essence Reaver and Iceborn Gauntlet

I was just playing Ezreal and I had Ionian Boots of Lucidity, Iceborn Gauntlet, and Essence Reaver giving me more than the total 40% cdr. However, when I sold my boots, the stat indicator next to my champion picture dropped my cdr down to 30%, even though I still had Essence Reaver and Iceborn Gauntlet. I couldn't grab a screenshot apparently, although I pressed the buttons for it. Anyways, I figure what happened is with the cap of 40% the game saw I dropped 10% with the boots and subtracted that without processing the other items.