Welcome, and good question.
You do no gain access back. Yahoo has a two step verification, and if you have not provided a secondary method of verification, it is gone! I encourage you to always use a landline (non-mobile non-cellular) device to create accounts such as these. The provider always assume you are a responsible person, and you will never have your phone stolen, or your bill unpaid! On a landline, the will offer that OS another alternative method of recover, and you won't be distracted by the newness of your device and the excitement of having the internet in your hand while you are on the toilet! Just sayin!
Sit down , when you have the NEW DEVICE, and create the accounts on a landline, then add in the modile. that way, your account is not being controlled by the mobile, but it is your control, and you know how to get it back! Try it! Create an account on a desktop, then recover the account. THEN ADD In the mobile device!