Leibniz's Law for Sets
Let $S$ be an arbitrary set.
- $x = y \dashv \vdash x \in S \iff y \in S$
for all $S$ in the universe of discourse.
This is therefore the justification behind the notion of the definition of set equality.
A direct application of Leibniz's law.
Source of Name
This entry was named for Gottfried Wilhelm von Leibniz.