SQL UPDATE using SELECT

I have a table t1:

date        |     timestamp
                  2015-02-01 00:00:00
                  2015-02-01 00:00:00
                  2015-02-02 00:00:00
                  2015:02:03 00:00:00

I am trying to update the value in date, of just the date from timestamp.

This is what I am using:

update t1 set date = (select date(timestamp) from t1);

but it sets all values to the same as the 1st row?