Theorem fundmafv2rnb

Description: The alternate function value at a class A is defined, i.e., in the range of the function iff A is in the domain of the function. (Contributed by AV, 3-Sep-2022)

	Ref	Expression
Assertion	fundmafv2rnb	|- ( Fun F -> ( A e. dom F <-> ( F '''' A ) e. ran F ) )

Proof

Step	Hyp	Ref	Expression
1		funres	|- ( Fun F -> Fun ( F |` { A } ) )
2		dmafv2rnb	|- ( Fun ( F |` { A } ) -> ( A e. dom F <-> ( F '''' A ) e. ran F ) )
3	1 2	syl	|- ( Fun F -> ( A e. dom F <-> ( F '''' A ) e. ran F ) )