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Technically yes, every drain line must be vented and it's more essential on a washing machine drain than other drain lines. One purpose of a vent is to protect the trap on the drain from siphoning out. This is much more likely on an un-vented washing machine drain because the machine pumps the water out under pressure. All that said if you haven't had any sewer type odors in or around the washing machine then the drain may already be vented or it's not siphoning out the trap. I don't know on what authority this plumber is making this demand but generally no code enforcement official is going to come to your house and require that this venting work be done.