Theorem afvvdm

Description: If the function value of a class for an argument is a set, the argument is contained in the domain of the class. (Contributed by Alexander van der Vekens, 25-May-2017)

	Ref	Expression
Assertion	afvvdm	|- ( ( F ''' A ) e. B -> A e. dom F )

Proof

Step	Hyp	Ref	Expression
1		ndmafv	|- ( -. A e. dom F -> ( F ''' A ) = _V )
2		nvelim	|- ( ( F ''' A ) = _V -> -. ( F ''' A ) e. B )
3	1 2	syl	|- ( -. A e. dom F -> -. ( F ''' A ) e. B )
4	3	con4i	|- ( ( F ''' A ) e. B -> A e. dom F )