Bathroom and laundry drain system

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randomwyoguy

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Remodeling a small bathroom and adding a washer and dryer. Is the junction shaded in red below acceptable and safe? It would be a 3 inch wye that connects the shower and washer drains to the waste pipe which then flows to the main stack. My only concern the wye may impede flow from the toilet. The photo is a plan view and is not to scale. The washing machine and shower drain pipes are 2". I appreciate any feedback.
drain system.jpg
 
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