Theorem dmsnop

Description: The domain of a singleton of an ordered pair is the singleton of the first member. (Contributed by NM, 30-Jan-2004) (Proof shortened by Andrew Salmon, 27-Aug-2011) (Revised by Mario Carneiro, 26-Apr-2015)

	Ref	Expression
Hypothesis	dmsnop.1	|- B e. _V
Assertion	dmsnop	|- dom { <. A , B >. } = { A }

Proof

Step	Hyp	Ref	Expression
1		dmsnop.1	|- B e. _V
2		dmsnopg	|- ( B e. _V -> dom { <. A , B >. } = { A } )
3	1 2	ax-mp	|- dom { <. A , B >. } = { A }