I am putting a bathroom in my basement.  Directly above the bathroom that I am constructing is existing plumbing coming from my shower/tub which hangs below my joists (and into my new bathroom's future ceiling.

I'll be replacing the trap (it is an old drum trap and all the piping is 1 1/2 copper) with new PVC.  My question is, can I angle my new piping  through the joists and then put the trap (and vent) about 3 to 4 feet away from the actual bathtub drain?  

The drain would still have a trap and vent, but just further away.  Is that OK?  What am I not thinking of?

 

Thanks!