Using Home Equity as Down Payment for Rental Property and Refi

[Robert Jensen]

Currently starting my brr journey and still learning. Main goal is to get to six rental properties as fast as possible. At the moment I am at the first r in brr on my first purchase. The house will soon be completely renovated so I am looking for ways to use the increased equity as a down payment for a duplex rental property. I will be looking at a minimum of $100k in equity to be used as the 20% on the duplex. 

I also just talked to the bank about refinancing(they called me) and they want to send an appraiser out to refinance on the new value of the house, which will remove the PMI and lower my monthly payment. I only put 3% down on this property and the banker said the equity could be used to essentially cover more, removing the PMI. My main concern though is that when I want to borrow on that equity I will not be able to because it will have been used towards the house to lower my payments? Am I wrong about this? Will refinancing have any effect on the amount I can borrow in six months towards my second BRR?

Thanks as usual, 

Robert