If you read the rule strictly, on July 15, your passport appears to meet all the requirements:
- It's been issued in the last ten years (by a single day, but still).
- It will be valid for more than three months after your departure.
Nowhere does it say that the two requirements should somehow be read conjointly or that the less-than-10-year-old requirement should apply for the whole stay (as opposed to the day of entry). At the same time, with many passports expiring after 10 years anyway, it's tempting to conclude that there is actually a requirement to hold a passport that would still be less than ten years old three months after leaving.
So while there are good reasons to think that you fulfil all the requirements, I think there is a moderate risk that a border guard might mistakenly think otherwise and I would not want to get in an argument about this stuff. Note that if you can get a new passport before you travel, it's perfectly fine to use it together with the visa in the old passport.