You can do anything you want with the cash out. The IRS could care less. However, the interest you pay on the cash out amount is "NOT" deductible on SCH A as an itemized deduction.
If you use all of that cash out to pay off a rental, then you can deduct the percentage of mortgage interest that applies to that amount on SCH E, and that could actually be beneficial down the road. Just understand that the tracing rules apply in case the IRS every questions you or audits you on it. Three rules to keep in mind on this stuff when dealing with the IRS:
1) You are GUILTY until proven innocent.
2) The burden of proof is on the accussed (that would be you!) and not the accuser.
3) If it's not in writing, then it *did* *not* *occur*.
