when was the existance of "air" proven?

Answer 1

The concept of air reaches far back into history, the earliest recorded would be Enlil, the air god of the Sumerians. It is one of the "five elements" proposed by Aristotle, and similarily by the Chinese ("wood" is often equated to air). It was thought that air becomes fire when heated, and water when cooled.

"Air" in its modern sense would be defined as the layer of gases surrounding the Earth's atmoshpere. It is difficult to trace the "discovery" of air to any one date, but the discovery of oxygen may prove to be the best estimate.

Oxygen was first described in the 16th century by Sędziwój, a Polish alchemist, and later, more accurately by Scheele in 1773.

Answer 2

Otto von Guericke in 1650. He made two copper hemispheres and also made a vacuum pump. When the air inside the two hemispheres was taken out a team of eight horses couldn't pull apart the spheres.

That proved that the hemispheres were pushed together by the pressure of a surrounding fluid (the surrounding air pressure).