**Description: **Axiom of Quantified
Negation. Axiom C5-2 of [Monk2] p. 113. This
axiom
scheme is logically redundant (see ax10w 1992) but is used as an auxiliary
axiom scheme to achieve scheme completeness. It means that 𝑥 is not
free in ¬ ∀𝑥𝜑. (Contributed by NM, 21-May-2008.)
Use its alias
hbn1 2006 instead if you must use it. Any theorem in
first order logic (FOL)
that contains only set variables that are all mutually distinct, and has
no wff variables, can be proved *without* using ax-10 2005 through ax-13 2233,
by invoking ax10w 1992 through ax13w 1999. We encourage proving theorems
*without* ax-10 2005 through ax-13 2233 and moving them up to the ax-4 1727
through
ax-9 1985 section. (New usage is
discouraged.) |