Question

What evidence do we have that distant galaxies are moving away from us?

Answer 1

... because Edwin Hubble was the man that proved it from his observations. He proved that there is a direct relationship between the speeds of distant galaxies and their distances from Earth. This is now known as Hubble's Law.

Step-by-step explanation:

Answer 2

Using the redshift of electromagnetic spectra you can determine the current distance and speed of remote galaxies. Observing the same galaxies over time you can determine that the galaxies are moving away from us and accelerating. You will also note that their speed is proportional to their distance (the further away they are the faster they are moving), which is a feature of metric expansion.

Step-by-step explanation: