water softener drain

[Leemonster]

Hello, I'm planning an install for a water softener in my basement and want to make sure I can plumb in a drain properly. I have an existing drain pipe that currently handles a bathroom and washer that I want to tie into. I've attached a picture. I'm thinking I can just cut into this and install a p trap and standpipe for the softener drain. Does anyone see any problems with this? Any ideas or criticisms are welcome Thanks.