If I move to Texas, I will need air conditioning. I don't need air conditioning. So I didn't move to Texas" is an argument form known as

modus tollens

This argument form is known as modus tollens.

The argument form you mentioned is called Modus Tollens. It follows the standard structure of a logical argument known as a syllogism. Modus Tollens is a valid logical argument and can be summarized as follows:

1. If A, then B. (If I move to Texas, then I will need air conditioning.)
2. Not B. (I don't need air conditioning.)
3. Therefore, not A. (So, I didn't move to Texas.)

In this case, you are using Modus Tollens to reason that since you don't need air conditioning (not B), you didn't move to Texas (not A).