Definition·D103
Logical axiom
A formula is a logical axiom exactly when it is a propositional, quantifier, or equality axiom instance.
For a language
:
is a logical axiom
it is a propositional axiom, a quantifier axiom, or an equality axiom.
In words
A formula of the language is a logical axiom exactly when it is one of the three kinds already characterized: propositional, quantifier, or equality.
Rests onno axioms yet
Never needed: F02 · F03 · F04 · F05 · F06 · F08 · F09 · F10 · F11 · F12 · F13 · F14 · A01 · A02 · A03 · A04 · A05 · A06 · A07 · A08 · A09 (computed from the citation graph, not asserted).
Remarks
Purely an umbrella over the three prior definitions - no new mathematical content, just naming the union so a proof can cite "logical axiom" once instead of three separate cases every time. Every logical axiom is valid in every structure, under every assignment - proved once, case by case over these same three kinds.