No, diagram one show the washer being dumped down the laundry tray vent.
You need to move the tee for the washer "below" the tee for the laundry tray.
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The washer comes in "below" the laundry tray.
why does the washer drain require a lower connection, it it because the laundry is a 2" drain and the sink is a 1.5", largest drain goes lowest?