Talk to the many fine agents responding to your question.
The answer is yes, you can.
One can do a cash out refinance, or a home equity loan.
There are other complex instruments one can use, but the above will be the easiest.
OMG! You cannot borrow money for a down payment! FHA, nope, RD Nope, VA Nope, Conventional NOPE
Where do you people get your info??
Be prepared to pay two mortgages for a few months, depending on how long it takes to close on the house you're selling. You can get an idea of how long your property is expected to be on the market through your Realtor.
You may also have some expenses getting the bridge, such as appraisal, and closing costs; sometimes the expenses are rolled into the loan and no cash will be do. Also look into getting the bridge with the same lender you will get the primary from. This may help simplify the process too,
If you have the ability to go this route, it will likely help make the move a lot less stressful or complicated.
Keep in mind that you will have to budget for continued insurance and loan payments for both properties for the length of time t takes to sell the first house.
When you are ready to close on the first home you will be required to pay off the line of credit just as you would any lien.
You cannot borrow ( which IS a bridge loan) the down payment for a mortgage!! Thats real estate 101
Also, since you already have a house, the 2nd home will probably be considered as an investment property if with in 100 miles or so, and you will need around 25% down for the down payment
You should contact your bank for finaning options