By distilling it you remove all impurity so yes it's just hydrogen & Oxygen, Water in a stream will usually be mostly rainwater so that actually scores lower in impurity than your tap water, It's why cats & dogs drink from puddles rather than choose a nice fresh bowl of tap water you have put down yards away. They know it's better water they can taste it & it does a better job of quenching their thirst. Rainwater is natures own distilled water if you collect it after it's been raining for 30 minutes it will be measured at zero impurity it takes 30 minutes of good rain to clean the air pollution. The Sun boils the rain into moisture & it falls from the clouds perfectly distilled. It's the only water with a negative charge this means electricity flows through it at a fraction of the speed it's why we use it in car battery's not just for the conductivity of the electricity but for the lifespan of the battery if you put tap water in your battery it won't live for very long.
We run on electrolytes which are basically electrons that flow round our nervous system omitting charges to our brain which is made of 90% water & this process we call thought.
Minerals are hard deposits that sit in your capillaries & joints & cause all manner of diseases.
Try a 2 week detox drinking only distilled water you will literally feel the impurity leaching from your pores in the way of an itchy rash that can last up to a few days depending on the level of impurity in your blood stream. After 2 days it just disappears & what you have done is performed dialysis on yourself. It's exactly how a dialysis machine works it cleans blood with distilled water.
Doctors ought to be shouting it from the rooftops but there isn't any commission in selling you something that falls from the sky for free. Chemotherapy on the other hand has a lovely profit margin.