Axiom 5 for predicate logic: If p
does not contain an occurrence of x
(note that (p: wff)
in contrast to (p: wff x)
means that p
cannot
depend on variable x
), then p
implies A. x p
because the quantifier is trivial.
axiom ax_5 {x: nat} (p: wff): $ p -> A. x p $;