Quick way of checking inner product

Question

If we want to determine whether or not an object has a list of properties, we can always just go down the list and check whether or not each individual property holds. But sometimes in linear algebra we have theorems that allow us to do this process more efficiently. For example to prove a subset of a vector space itself has all the properties of a vector space, it is sufficient simply to prove it is closed under vector addition and scalar multiplication. Or if a linear transformation is an operator on a finite dimensional space, checking whether it has just one of invertibility, injectivity, or surjectivity is sufficient for checking all three. Is there any analogous situation where we can prove a function is/isn’t an inner product by checking a shorter list of conditions than checking linearity, positive-definiteness, and conjugate symmetry?