It is the voice of classical logic, as we are taught at wormingers' school.
For classical logic, it can be easily verified with a truth table.
It is considered to be a law of classical logic.
This is similar to a way of axiomatizing classical propositional logic.
In classical logic, we often discuss the truth values that a formula can take.
In classical logic, the additional notion of soundness is introduced.
There is no third truth-value, at least not in classical logic.
See more details about functional completeness in classical logic at Truth function.
To put it in more precise mathematical terms, classical logic has two values.
However, there is a close relationship between the two in most logics, including classical logic.