No, when the WM was running, it would siphon the proposed shower drain dry. EACH trap needs a vent. Depending on how big that pipe is, you might be able to do it IF you added a vent, but a WM drain line can be problematic. You don't want sudsy water getting pumped into your shower!
Thanks for the answer.
I know very little about drains but I'm trying to remove a shower wall that contains a vent. (the green wall in the diagram)
Would there be too many bends in the line to bring the shower drain to the vent in wall A and from there back to the current drain below the green wall?
If you look at your first drawing you will note that the vents are vertical. They have to be that way to ensure that no waste ever backs into the vent and stays there.
Thanks.
I'm starting to understand.
I do have a sink drain with a vent that is vertical but it would be a 6ft run from the shower trap.
Is that too far?
The vent must come off of the trap arm before the waste turns down, and must be within 5' with a 2" pipe. It must go vertical before it can go horizontal.
You could say that the drain upstream of the proposed pink drain could be a wet vent, and providing that that drain is 1.5", then it can take up to 2FU (fixture units) which would cover the washing machine. You just have to make sure the distance from the trap of the shower to the proposed wet vent would be more than 2 x the diameter of the drain pipe (so probably 3 inches).