As this article explains, the concept of alcohol proof is simple: "Double the number listed as the alcohol by volume on the bottle. A spirit with 40 percent alcohol by volume, therefore, is 80 proof."
Thus, if you know the alcohol content on a volume basis, the "proof number" is really redundant.
The historical origins are interesting:
In the 18th century, proof was much more straightforward. Liquor was "proofed" at the distillery by adding gunpowder and lighting it on fire. If it didn't light, the alcohol content was too weak. If it burned yellow, too strong. If it burned blue, the proof was just right (that was around 57 percent, or 114 proof).The flash point (the temperature at which a volatile material can form combustible vapors) of a 60% alcohol-water mixture is 22 C - which perhaps explains its historical antecedents. It also explains why some high proof spirits have flame retardants.