Depends on what code your town, county, or state uses- it varies

 

How do I find that out? Is there a general national code?

 

You are IPC https://www.gainesville.org/DocumentCenter/View/177/Building-Code-Book-Purchasing-PDF
I can not help with cloths washers for that code- sorry
@Ghostmaker can if he pops in

 

Also here https://www.gainesville.org/DocumentCenter/View/175/2021-Building-Code-Changes-PDF
Maybe call your city Govt. office and ask for a plumbing inspector to assist you

 

Your under IPC I'm a plumbing inspector in Ohio that uses IPC. How can I help you? Your washer drain could be either size depending on how one is piping it. Could you draw a diagram for me?

 

 

In the drawing you have provided that installation would be non compliant to IPC plumbing code. A washer machine is not an approved wet vent fixture to be used to vent a toilet. You cannot replace the lavatory sink with a washer machine and be code compliant.

912.1 Horizontal wet vent permitted. Any combination of fixtures within two
bathroom groups located on the same floor level is permitted to be vented by a
horizontal wet vent. The wet vent shall be considered the vent for the fixtures and
shall extend from the connection of the dry vent along the direction of the flow in
the drain pipe to the most downstream fixture drain connection to the horizontal
branch drain. Each wet-vented fixture drain shall connect independently to the
horizontal wet vent. Only the fixtures within the bathroom groups shall connect to
the wet-vented horizontal branch drain. Any additional fixtures shall discharge
downstream of the horizontal wet vent.

BATHROOM GROUP. A group of fixtures consisting of a water closet,
lavatory, bathtub or shower, including or excluding a bidet, an emergency floor
drain or both. Such fixtures are located together on the same floor level

To install the washer you would need to reinstall the lavatory sink and then tie the washer in downstream of your toilet on its own branch.

 

Sorry, I didn’t include all of my drains.
I want to hang a toilet, a washing machine, and a laundry sink. The wall that the sink is on is an adjacent wall. Hopefully my picture makes sense. I thought that I could use the existing 3 inch coming down from my upstairs as a vent for the toilet and then have the sink and washing machine have their own vents.