An axiom schema is valid if and only if every instance of the schema is valid. The schema above is valid, as are the schemas shown below.
Reflexivity | φ ⇒ φ |
Negation Elimination | ¬¬φ ⇒ φ |
Negation Introduction | φ ⇒ ¬¬φ |
Tautology | φ ∨ ¬φ |
In what follows, we use both non-valid and valid axiom schemas. Non-valid schemas play a role in defining rules of inference, and valid schemas are used as components of deductive proof systems.
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