The following extract is from Relativity Simply Explained by Martin Gardner (Amazon link):
Consider an astronaut in a spaceship that is racing alongside a light beam. The ship is traveling with half the speed of light. The astronaut will find, if he makes the proper measurements, that the beam is still passing him at its usual velocity of 299,800 kilometers per second! Think about this for a moment and you will soon realize that this must indeed be the case if the notion of an ether wind is discarded. If the astronaut found that light slowed down relative to his motion, he would have detected the very ether wind that Michelson and Morley failed to detect. Similarly, if his spaceship travels directly toward a source of light, moving with half the speed of light, will he find the beam approaching him twice as fast? No, it is still moving toward him at 299,800 kilometers per second. Regardless of how he moves relative to the beam, his measurements will always give the beam the same speed
I cannot follow the reasoning of this statement. The Michelson and Morley experiment proved that there was no ether wind, but I cannot see how it proves anything else.