Your Grace, you are in the presence of Daenerys Stormborn of House Targaryen, the First of Her Name, Queen of the Andals and the First Men, the Unburnt, Queen of Dragon’s Bay, Khaleesi of the Great Grass Sea, Breaker of Chains and Mother of Dragons.“
I’ve always been a firm believer that both Jon and Dany are the prince that was promised and during the episode I got confirm of it and that’s why: it’s all about the Valyrian word. Like Missandei said it’s gender neutral and it translates as both prince and princess. That’s it, in the prophecy they used one word to indicate two things at the same time because the word can be applied to both. This way there’s no need to repeat it twice. If you think about it it’s so obvious.
Just wanted to add, for those who believe that only Jon is the Prince that was promised: you’re ignoring the most obvious hint that points towards Daenerys: “He/She shall wake dragons out of stone.” That’s Dany, there’s no way to deny it.