Very nicely put Moreless, but rainwater has much more in it than distilled water:
From one of my posts in water debate forum (with an edit):
“I would also like to point out to you that rainwater is really not like distilled water at all! It appears that raindrops do carry a trace amount of minerals (see study below); also I suspect that the fall from the clouds through the air has an effect on the rainwater’s molecular structure and as it passes through the oxygenated atmosphere, sunlight and the magnetic field it is transformed in a way that distilled water cannot compare to!
Studies of the chemical composition of rainfall have been carried on for many years starting in late 1880s in the United States and in Europe. Rainwater collected in various parts of the USA contains (in milligrams per liter): Fe (0.015) , Ca (0.075-1.41), Mg (0.027-1.2), Na (0.22-9.4), Ca (0.075-1.41), K (0.072-0.11), HCO3 (4-7), SO4 0.7-7.6), Cl (0.22-17), NO2 (0.02), NO3 (0.02-0.62), and Total Dissolved Solids 8.2-38), and pH of 4.9 to 6.4.”