Theorem fnsn

Description: Functionality and domain of the singleton of an ordered pair. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypotheses	fnsn.1	|- A e. _V
	fnsn.2	|- B e. _V
Assertion	fnsn	|- { <. A , B >. } Fn { A }

Proof

Step	Hyp	Ref	Expression
1		fnsn.1	|- A e. _V
2		fnsn.2	|- B e. _V
3		fnsng	|- ( ( A e. _V /\ B e. _V ) -> { <. A , B >. } Fn { A } )
4	1 2 3	mp2an	|- { <. A , B >. } Fn { A }