Theorem xpsn

Description: The Cartesian product of two singletons is the singleton consisting in the associated ordered pair. (Contributed by NM, 4-Nov-2006)

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

Proof

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