Description: Axiom of Existence. One of the equality and substitution axioms of
predicate calculus with equality. This axiom tells us is that at least
one thing exists. In this form (not requiring that x and y be
distinct) it was used in an axiom system of Tarski (see Axiom B7' in
footnote 1 of KalishMontague p. 81.) It is equivalent to axiom scheme
C10' in Megill p. 448 (p. 16 of the preprint); the equivalence is
established by axc10 and ax6fromc10 . A more convenient form of this
axiom is ax6e , which has additional remarks.

ax-6 can be proved from the weaker version ax6v requiring that the
variables be distinct; see theorem ax6 .

ax-6 can also be proved from the Axiom of Separation (in the form that
we use that axiom, where free variables are not universally quantified).
See theorem ax6vsep .

Except by ax6v , this axiom should not be referenced directly. Instead,
use theorem ax6 . (Contributed by NM, 10-Jan-1993)(New usage is discouraged.)