The singleton of a set $a$ is
\[\{a\} = \{a, a\}.\]
For any set $X$,
\[X \neq \{X\}.\]
Proof. If $X = \{X\}$, then $X \in X$, contrary to irreflexivity of $\in$.
The singleton of a set $a$ is
\[\{a\} = \{a, a\}.\]
For any set $X$,
\[X \neq \{X\}.\]
Proof. If $X = \{X\}$, then $X \in X$, contrary to irreflexivity of $\in$.