Again, you can choose to view things however you want. Ohm's Law is very simple (for most people) to comprehend. It states that the current through the conductor is proportional to the voltage across the conductor. Look it up. Thus, if you double the voltage across the conductor, the current through the conductor doubles. This is what proportional means. Look it up. Mathematically, this means thatHmm...

You change your avatar but, apparently, you can't change your hostile demeanor when your point of view is questioned.

The point is that regardless of the properties of the material, be it an insulator, a semiconductor, or a conductor, if it isn't forced into superconductivity, Ohm's law can always be used to determine the voltage across, the current through, or the resistance of a chunk of material at any instant in time if two of the three quantities are known. And, for the purpose of responding to the OP's query, it's perfectly fine to consider the transformer as a perfect transducer where power out equals power in.

current = k * voltage

where k is a constant of proportionality. Notice the word "constant". If k is NOT a constant, then the relationship between the current and the voltage is no longer proportional and Ohm's Law does not apply. In practice, k is never a perfect constant over all conditions, but if the changes in k over the range of interest are small enough, then k is close enough to being a constant for that material to be considered ohmic (for that purpose over that range of conditions). If it is NOT close enough to being a constant, then you can call the ratio of V/I to be anything you want, including R, but it is NOT the R that is the proportionality constant in Ohm's Law (where R = 1/k in the above equation). You are perfectly free to pretend otherwise, but that doesn't make it so.