If your question is how do we know that the definition of air is "Hevel," the answer is that this is clear from many Gemaros. A proof that is "in season" is the Sifri d'Agadata on Esther which famously says that the world exists on "Hevel Pihem Shel Tinokos Beis Raban" -- "the air of the words of the children who learn Torah."

If you are asking about how we see that bad air kills, I admittedly have not gone into the subject much. However, Rav Moshe Feinstein in Igros Moshe (CM 1:99) says that according to Rav (that Hevel presumably kills), it is not that Rav holds that every ten Tefach deep pit will kill. Rather, Rav holds that the Torah established a novel law that whenever there is a ten tefach deep pit which has Hevel, as long as the Hevel contributed in some way to the animal's death, even if it unquestionably could not have caused the death on its own, the owner of the pit is liable for the damage. Accordingly, even if the air weakened it when it was falling (any pit that is deeper than it is wide will have limited air, restricting oxygen and possibly adding other fumes, thereby weakening a person or animal) this is enough to make the owner liable for its death. [See the Igros Moshe inside for a deeper understanding of how this applies to the Gemara.]

All the best,

Yaakov Montrose