Yes, PROVES is a Scrabble word!

Letter values in Scrabble US: P 3, R 1, O 1, V 4, E 1, S 1.

Is it a valid word?

PROVES is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

be shown or be found to be
establish the validity of something, as by an example, explanation or experiment
provide evidence for
prove formally; demonstrate by a mathematical, formal proof
put to the test, as for its quality, or give experimental use to
increase in volume
cause to puff up with a leaven
take a trial impression of
obtain probate of

Also: turn out, turn up, bear witness, try out.