Boarding pass. Reservation does not mean a thing for proof of travel.

this works too: https://www.aa.com/your-receipts/

From AA website: To find your ticket number, check the email we sent you when you booked your trip, your cancellation email, or your credit card statement.

Your ticket number is a unique 13-digit number that identifies your reservation. The first 3 digits of your ticket number are the airline code, which is always ‘001’ for American Airlines.

Example ticket number: 001234567890