How was Edwin Hubble able to use his discovery of a Cepheid in Andromeda to prove that a spiral nebulae were actually individual galaxies?
In 1908, H. S. Leavitt found that Cepheid variables can be used as distance indicators. There is a relation between the pulsation period and luminosity, so they can be used as 'standard candles'.
After studying a Cepheid in the Andromeda galaxy, Hubble determined the distance and found out that it is not part of the Milky Way but another galaxy. The distance was too large for it to be part of the Milky Way.