Theorem afvvfunressn

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

	Ref	Expression
Assertion	afvvfunressn	|- ( ( F ''' A ) e. B -> Fun ( F |` { A } ) )

Proof

Step	Hyp	Ref	Expression
1		nfunsnafv	|- ( -. Fun ( F |` { A } ) -> ( F ''' A ) = _V )
2		nvelim	|- ( ( F ''' A ) = _V -> -. ( F ''' A ) e. B )
3	1 2	syl	|- ( -. Fun ( F |` { A } ) -> -. ( F ''' A ) e. B )
4	3	con4i	|- ( ( F ''' A ) e. B -> Fun ( F |` { A } ) )