The Black Mamba's daughter is now a cardinal and gold Trojan ... Natalia Bryant just got accepted into USC on Tuesday -- and Vanessa says Kobe would've been "so proud!"
Vanessa shared the amazing news with heartwarming videos ... showing a PUMPED Natalia after she got her acceptance letter into the University of Southern California.
In one of Vanessa's vids of the special moment, 18-year-old Natalia jumped up and down over and over again ... and screamed "I got in!" repeatedly.
In the other Vanessa video, she showed off all the gifts she gave Natalia for the accomplishment .