There are a number of qualifications to all that.
First, this is only between two applicants for patents.
Second, invention is conception plus reduction to practice. You have to not only document conception but also a working prototype. Date of invention is the date of the working prototype (or the filing of an enabling patent application). If you can show an unbroken chain of due diligence from the date of conception to the date of your first working prototype and/or the filing of the patent application, then -- and only then -- is your conception date your date of invention.
Third, the prior inventor only prevails in US law if they have not "abandoned, suppressed, or concealed" their invention.
35 USC 102(g).
Fourth, for a provisional application to provide any proof of invention, the provisional application must do more than just prove conception -- it must also be enabling of the invention as claimed. In other words, it must meet the very same legal standard for sufficiency as does a non-provisional application.
In short, here's my advice for those not deeply familiar with all the nuances and subtleties of US patent law. Treat the US as a first-to-file country and forget about provisional applications.
Regards.