Is there a Mewtwo event in Pokemon soul silver?

To get mewtwo in soulsilver, you must first beat the elite four, possibly some other things, then go t cerulean city. Go over the bridge, (the gold one, north of the city) then go to the left. surf on the water. (down, left, down, left, so on,) until you get to a cave. You will need rock smash. Enter the cave, and explore. After a while of exploring, you will end up in the basement, (after going to the second floor) and the surf, mewtwo is somewhere down there.