pvc piping for washing machine drain

I recently removed a tub from my claw-foot tub from my bathroom in order to install a washing machine. The drain from the tub is still there, attached to an upright piece of pvc. How do I remove the horizontal tub drain and add to the vertical drain in order to properly drain the washer? Right now I am doing small loads and draining into a bucket that I then empty into the sink.

The pipe is glued together and I don't want to break anything.

Ease of changing configurations of PVC is one of the big advantages of using it. You can not take joints apart, the pipe must be cut and appropriate fittings and pipes solvent glued where you want them. There are a couple of things about what you have that raise a couple of questions. The small size of the photos make it difficult to tell what size the pipe is. Typically tubs have only an 1-1/2" drain which is adaquate for a tub, but washers need a 2" drain due the the high volume of water discharged very quickly. In addition, I see no trap or vent, both of which are needed for the drain. By the way, you can't decrease the size of a drain as you head downstream.

pvc washer drain

The pvc is 2". There may be a trap under the floor? It is on a concrete slab. My previous residence had the same type of drainage system, but it was in the basement and drained under the floor to a floor drain.

My plan was to reuse the horizontal pipe to make the vertical pipe tall enough for the washer drain, and use the cap that was on top to close up the side.

Yes, there may be a trap under the slab, but you need for find out for sure. If you cut the PVC 3" or 4" above when it goes into the slab, then take a flashlight and look down into the drain. If there is a trap, you should see standing water. You still don't know about a vent, but if the tub was legally plumbed, there almost surely will be a trap and a vent. Since you have 2" pipe, you're pretty good to go. Nothing wrong with reusing pipe, just cut it to the lengths you need, clean and prime it, and glue it together with approprate fittings. If you cut the pipe as I mentioned above, use a coupler to connect a longer pipe to the cut end. (That's why you leave a stub when you cut.)