Yes. When the vehicle was purchased you depreciated the vehicle for business, whether in actual depreciation expense or the portion of the standard mileage rate that represents depreciation (if applicable). This means that you began to expense a part of the cost each year when it was placed in service for business, not when it was paid in full but while you were still paying for it.
Likewise, when you trade (sell for tax purposes) a vehicle for another vehicle whatever you receive in trade-in value is considered the business percentage of proceeds from the sale (selling price) regardless of what the funds were used for such as paying off the existing loan on the vehicle.
The IRS doesn't make us wait to expense an asset until it's paid in full, rather when we place the asset in service for business, rental, etc, regardless of the debt. We are required only to be liable for that debt. In other words we are the owner at the time we become liable for the debt that is incurred on any asset for tax purposes.
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