Theorem aovvdm

Description: If the operation value of a class for an ordered pair is a set, the ordered pair is contained in the domain of the class. (Contributed by Alexander van der Vekens, 26-May-2017)

	Ref	Expression
Assertion	aovvdm	|- ( (( A F B )) e. C -> <. A , B >. e. dom F )

Proof

Step	Hyp	Ref	Expression
1		df-aov	|- (( A F B )) = ( F ''' <. A , B >. )
2	1	eleq1i	|- ( (( A F B )) e. C <-> ( F ''' <. A , B >. ) e. C )
3		afvvdm	|- ( ( F ''' <. A , B >. ) e. C -> <. A , B >. e. dom F )
4	2 3	sylbi	|- ( (( A F B )) e. C -> <. A , B >. e. dom F )