I'm remodeling our bathroom and moving a washer and dryer to the room behind the bath. I've been reading through the posts, which have been very helpful and have a diagram I would love to get some feedback on. I am using some of the existing plumbing which was done a few years ago. I'm adding the washer, moving the WC and adding a utility sink.

A friend suggested that I connect the washer below the toilet to avoid bubbles. That is the reason for the parallel 3" line. Is that necessary? Also, do I have enough venting?

Thanks much for your time and feedback!