Theorem fvsn

Description: The value of a singleton of an ordered pair is the second member. (Contributed by NM, 12-Aug-1994) (Proof shortened by BJ, 25-Feb-2023)

	Ref	Expression
Hypotheses	fvsn.1	|- A e. _V
	fvsn.2	|- B e. _V
Assertion	fvsn	|- ( { <. A , B >. } ` A ) = B

Proof

Step	Hyp	Ref	Expression
1		fvsn.1	|- A e. _V
2		fvsn.2	|- B e. _V
3		fvsng	|- ( ( A e. _V /\ B e. _V ) -> ( { <. A , B >. } ` A ) = B )
4	1 2 3	mp2an	|- ( { <. A , B >. } ` A ) = B