Pulling equity out of rental property to buy personal residence?

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My fiancé and I have decided that we eventually want to own our own home within the next 5 years. I know the whole a home is not an asset argument, and I agree. But it would be better for our particular situation. Where I'm torn is the down payment. I don't want to use hard earned money for the down payment that could be put to better use buying more rental properties. The thought of saving up $60,000 and using it to buy something that doesn't produce a monthly return does not sit well with me. I'd like to pull equity out of my duplex and use that as the down payment on our house. I have approximately $162,000 in equity and an LTV of 55%. It would still cashflow fine with a higher payment. Will banks let me do this?