Theorem relsn

Description: A singleton is a relation iff it is an ordered pair. (Contributed by NM, 24-Sep-2013)

	Ref	Expression
Hypothesis	relsn.1	|- A e. _V
Assertion	relsn	|- ( Rel { A } <-> A e. ( _V X. _V ) )

Proof

Step	Hyp	Ref	Expression
1		relsn.1	|- A e. _V
2		relsng	|- ( A e. _V -> ( Rel { A } <-> A e. ( _V X. _V ) ) )
3	1 2	ax-mp	|- ( Rel { A } <-> A e. ( _V X. _V ) )