Description: Rule of existential generalization, similar to universal generalization
ax-gen , but valid only if an individual exists. Its proof requires
ax-6 in our axiomatization but the equality predicate does not occur
in its statement. Some fundamental theorems of predicate calculus can
be proven from ax-gen , ax-4 and this theorem alone, not requiring
ax-7 or excessive distinct variable conditions. (Contributed by Wolf
Lammen, 12-Nov-2017)(Proof shortened by Wolf Lammen, 20-Oct-2023)