How exactly did Brown v. Board of Education invalidate Plessy v. Ferguson?

Marshall (the NCAAP lawyer) used this case to get rid of “separate but equal”. Because there was no equal facilities for blacks. During the trial, Marshall used dolls (one black, one white) to prove his point: the segregation system is damaging black kids, giving them an inferiority complex to white kids. All the children (including blacks) picked the white doll instead of the black one.
The court, under anti racist Supreme Justice Warren, had a 9-0 decision to get rid of segregation in education.