Description: Axiom of Quantifier
Introduction. One of the equality and substitution
axioms of predicate calculus with equality. Informally, it says that
whenever is
distinct from and
, and
is true,
then quantified with is also true. In other words,
is irrelevant to the truth of
. Axiom scheme C9' in
[Megill]
p. 448 (p. 16 of the preprint). It apparently does not otherwise appear
in the literature but is easily proved from textbook predicate calculus by
cases.
This axiom is obsolete and should no longer be used. It is proved above
as Theorem ax12o 1934. (Contributed by NM, 5-Aug-1993.)
(New usage is discouraged.) |