Description: An alternate definition of double existential uniqueness (see 2eu4 ).
A mistake sometimes made in the literature is to use E! x E! y to
mean "exactly one x and exactly one y ". (For example, see
Proposition 7.53 of TakeutiZaring p. 53.) It turns out that this is
actually a weaker assertion, as can be seen by expanding out the formal
definitions. This theorem shows that the erroneous definition can be
repaired by conjoining A. x E* y ph as an additional condition. The
correct definition apparently has never been published. ( E* means
"there exists at most one".) (Contributed by NM, 26-Oct-2003) Avoid
ax-13 . (Revised by Wolf Lammen, 2-Oct-2023)