HRA Deduction

1. Yes, it is possible to claim HRA exemption u/s 10(13A) if you are truly paying rent for residing in city A. 
2. In fact, principal and interest can also be claimed as a deduction if the property in city B is purchased with the loan amount. 
3. In a nutshell, you can claim deductions u/s 10(13A) if you are paying rent and in receipt of HRA from the Employer. 
Please correct me if the above solution has an alternative view.