Theorem ndfatafv2undef

Description: The alternate function value at a class A is undefined if the function, whose range is a set, is not defined at A . (Contributed by AV, 2-Sep-2022)

	Ref	Expression
Assertion	ndfatafv2undef	|- ( ( ran F e. V /\ -. F defAt A ) -> ( F '''' A ) = ( Undef ` ran F ) )

Proof

Step	Hyp	Ref	Expression
1		ndfatafv2	|- ( -. F defAt A -> ( F '''' A ) = ~P U. ran F )
2		undefval	|- ( ran F e. V -> ( Undef ` ran F ) = ~P U. ran F )
3	2	eqcomd	|- ( ran F e. V -> ~P U. ran F = ( Undef ` ran F ) )
4	1 3	sylan9eqr	|- ( ( ran F e. V /\ -. F defAt A ) -> ( F '''' A ) = ( Undef ` ran F ) )