Theorem funsn

Description: A singleton of an ordered pair is a function. Theorem 10.5 of Quine p. 65. (Contributed by NM, 12-Aug-1994)

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

Proof

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