Description: A special instance of sp 2053
applied to an equality with a dv condition.
Unlike the more general sp 2053, we can prove this without ax-12 2047.
Instance of aeveq 1982.
The antecedent with distinct and is a
characteristic of a degenerate universe, in which just one object
exists. Actually more than one object may still exist, but if so, we
give up on equality as a discriminating term.
Separating this degenerate case from a richer universe, where inequality
is possible, is a common proof idea. The name of this theorem follows a
convention, where the condition is denoted by 'aev', a
shorthand for 'all equal, with a distinct variable condition'.
(Contributed by Wolf Lammen, 14-Mar-2021.) |