Yes, the statement is true that oxygen a planet's atmosphere is smoking gun evidence for life on earth.
If there were no life on the planet, then all the oxygen would be converted into carbon dioxide - the chief component of the greenhouse effect.
Without life, there would be low levels of oxygen or an end of oxygen in the atmosphere and a resultant abundance of carbon dioxide.
Excessive levels of carbon dioxide are creating the greenhouse effect which is ultimately leading to global warming.
Moreover, the planet earth would be hotter just like venus as there is no oxygen.
Furthermore, there will be sulfur and nitrogen oxides in the atmosphere resulting in acidic rain.
If we look back into the earth's history, we see that organisms such as microbes, algae, and fungi are the ultimate producers of oxygen in the atmosphere through photosynthesis which is smoking gun evidence for life on the planet.
To put it simply, oxygen is extremely important for the respiration, growth, and development of living things.
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