Theorem bj-axsn

Description: Two ways of stating the axiom of singleton (which is the universal closure of either side, see ax-bj-sn ). (Contributed by BJ, 12-Jan-2025) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-axsn	|- ( { x } e. _V <-> E. y A. z ( z e. y <-> z = x ) )

Proof

Step	Hyp	Ref	Expression
1		velsn	|- ( z e. { x } <-> z = x )
2	1	bj-clex	|- ( { x } e. _V <-> E. y A. z ( z e. y <-> z = x ) )