This is true, assuming no mutations. Mutations are not desirable because they come with disease and disorder.

The Y chromosome has been passed down from father to son for generations, tracing all men back to a common patriarch.

For something so tiny, the Y chromosome is fascinating in a lot of ways. It is passed virtually unchanged from father to son (women do not have this chromosome). source: thetech.org

The Y chromosome does not mix with DNA from the mother, since she does not have a Y chromosome.

All scientific evidence points to the fact that if you go far enough back, all life on Earth is related through common ancestry. Turns out that applying the same sort of analysis shows that all humans alive today are descendants of one man and one woman who walked our planet thousands of years ago. source: arstechnica.com