simple venting question

hello, could anyone tell me if i need to add a curcuit vent to the right of the sink drain in this photo?
that's a washer drain on the far right, a separate lav on the far left. the drain in the middle is the one in question. do i need a vent between it and the washer drain that Tees into the vent stack up where i have those double ells?
i hope i've done both the venting and this posting correctly. it's my first(posting).
thanks in advance

I would have put another sanitary tee for the sink drain on top of the one for the washer. The way you have it, the washer draining is going to siphon the sink's trap.

thanks for the response cacher. i'm a little dense, but i think i follow. so there would be two lateral arms flowing to the stack? being more of a carpenter, i'd love to try and avoid all those holes in the framing.
btw, what part of wisconsin?

Correct, 2 separate arms. You will need to make sure they are installed low enough for the sink that you plan to use.

I am from NW WI, but am currently between Milwaukee & Chicago.

It's common for a laundry tray and washer to be plumbed together.

If the washer is plumber over the sink, it will siphon the trap.

There is more than one problem with having the sink drain installed where and how you show it. The vent would have to be ON the sink drain before it connects to the horizontal line, to start with.